Lecture notes in applied differential equations of mathematical physics /:
Functional analysis is a well-established powerful method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and statistical turbulence. This book presents a unique, modern treatment of solutions to fractional random differential equat...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, N.J. :
World Scientific Pub. Co.,
©2008.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Functional analysis is a well-established powerful method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and statistical turbulence. This book presents a unique, modern treatment of solutions to fractional random differential equations in mathematical physics. It follows an analytic approach in applied functional analysis for functional integration in quantum physics and stochastic Langevin-turbulent partial differential equations. |
| Beschreibung: | 1 online resource |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9789812814586 9812814582 |
Internformat
MARC
| LEADER | 00000cam a2200000Ma 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn820944533 | ||
| 003 | OCoLC | ||
| 005 | 20240705115654.0 | ||
| 006 | m o d | ||
| 007 | cr cn||||||||| | ||
| 008 | 090522s2008 si a ob 001 0 eng d | ||
| 040 | |a LGG |b eng |e pn |c LGG |d OCLCO |d N$T |d IDEBK |d DEBSZ |d YDXCP |d OCLCQ |d OCLCF |d OCLCQ |d AGLDB |d OCLCQ |d MERUC |d ZCU |d U3W |d STF |d OCLCQ |d VTS |d ICG |d INT |d OCLCQ |d TKN |d OCLCQ |d DKC |d AU@ |d OCLCQ |d M8D |d UKAHL |d OCLCO |d OCLCQ |d OCLCO |d OCLCL | ||
| 019 | |a 1086427416 | ||
| 020 | |a 9789812814586 |q (electronic bk.) | ||
| 020 | |a 9812814582 |q (electronic bk.) | ||
| 020 | |z 9789812814579 |q (hbk.) | ||
| 020 | |z 9812814574 |q (hbk.) | ||
| 035 | |a (OCoLC)820944533 |z (OCoLC)1086427416 | ||
| 050 | 4 | |a QC20.7.D5 | |
| 072 | 7 | |a MAT |x 007000 |2 bisacsh | |
| 082 | 7 | |a 515.35 |2 22 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Botelho, Luiz C. L. | |
| 245 | 1 | 0 | |a Lecture notes in applied differential equations of mathematical physics / |c Luiz C.L. Botelho. |
| 260 | |a Singapore ; |a Hackensack, N.J. : |b World Scientific Pub. Co., |c ©2008. | ||
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Ch. 1. Elementary aspects of potential theory in mathematical physics. 1.1. Introduction. 1.2. The Laplace differential operator and the Poisson-Dirichlet potential problem. 1.3. The Dirichlet problem in connected planar regions: a conformal transformation method for green functions in string theory. 1.4. Hilbert spaces methods in the Poisson problem. 1.5. The abstract formulation of the Poisson problem. 1.6. Potential theory for the wave equation in R[symbol] -- Kirchhoff potentials (spherical means). 1.7. The Dirichlet problem for the diffusion equation -- seminar exercises. 1.8. The potential theory in distributional spaces -- The Gelfand-Chilov method. | |
| 505 | 0 | |a Ch. 2. Scattering theory in non-relativistic one-body short-range quantum mechanics: Möller wave operators and asymptotic completeness. 2.1. The wave operators in one-body quantum mechanics asymptotic properties of states in the continuous spectra of the Enss Hamiltonian. 2.2. The Enss proof of the non-relativistic one-body quantum mechanical scattering -- ch. 3. On the Hilbert space integration method for the wave equation and some applications to wave physics. 3.1. Introduction. 3.2. The abstract spectral method -- the nondissipative case. 3.3. The abstract spectral method -- the dissipative case. 3.4. The wave equation "path-integral" propagator. 3.5. On the existence of wave-scattering operators. 3.6. Exponential stability in two-dimensional magneto-elasticity: a proof on a dissipative medium. 3.7. An abstract semilinear Klein Gordon wave equation -- existence and uniqueness. | |
| 505 | 0 | |a Ch. 4. Nonlinear diffusion and wave-damped propagation: weak solutions and statistical turbulence behavior. 4.1. Introduction. 4.2. The theorem for parabolic nonlinear diffusion. 4.3. The hyperbolic nonlinear damping. 4.4. A path-integral solution for the parabolic nonlinear diffusion. 4.5. Random anomalous diffusion, a semigroup approach -- ch. 5. Domains of Bosonic functional integrals and some applications to the mathematical physics of path-integrals and string theory. 5.1. Introduction. 5.2. The Euclidean Schwinger generating functional as a functional Fourier transform. 5.3. The support of functional measures -- the Minlos theorem. 5.4. Some rigorous quantum field path-integral in the analytical regularization scheme. 5.5. Remarks on the theory of integration of functionals on distributional spaces and Hilbert-Banach spaces. | |
| 505 | 0 | |a Ch. 6. Basic integral representations in mathematical analysis of Euclidean functional integrals. 6.1. On the Riesz-Markov theorem. 6.2. The L. Schwartz representation theorem on [symbol] (distribution theory). 6.3. Equivalence of Gaussian measures in Hilbert spaces and functional Jacobians. 6.4. On the weak Poisson problem in infinite dimension. 6.5. The path-integral triviality argument. 6.6. The loop space argument for the thirring model triviality -- ch. 7. Nonlinear diffusion in R[symbol] and Hilbert spaces: a path-integral study. 7.1. Introduction. 7.2. The nonlinear diffusion. 7.3. The linear diffusion in the space [symbol]. | |
| 505 | 0 | |a Ch. 8. On the Ergodic theorem. 8.1. Introduction. 8.2. On the detailed mathematical proof of the RAGE theorem. 8.3. On the Boltzmann Ergodic theorem in classical mechanics as a result of the RAGE theorem. 8.4. On the invariant Ergodic functional measure for some nonlinear wave equations. 8.5. An Ergodic theorem in Banach spaces and applications to stochastic-Langevin dynamical systems. 8.6. The existence and uniqueness results for some nonlinear wave motions in 2D -- ch. 9. Some comments on sampling of Ergodic process: an Ergodic theorem and turbulent pressure fluctuations. 9.1. Introduction. 9.2. A rigorous mathematical proof of the Ergodic theorem for wide-sense stationary stochastic process. 9.3. A sampling theorem for Ergodic process. 9.4. A model for the turbulent pressure fluctuations (random vibrations transmission). | |
| 505 | 0 | |a Ch. 10. Some studies on functional integrals pepresentations for fluid motion with random conditions. 10.1. Introduction. 10.2. The functional integral for initial fluid velocity random conditions. 10.3. An exactly soluble path-integral model for stochastic Beltrami fluxes and its string properties. 10.4. A complex trajectory path-integral representation or the Burger-Beltrami fluid flux -- ch. 11. The Atiyah-Singer index theorem: a heat kernel (PDE's) proof. | |
| 520 | |a Functional analysis is a well-established powerful method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and statistical turbulence. This book presents a unique, modern treatment of solutions to fractional random differential equations in mathematical physics. It follows an analytic approach in applied functional analysis for functional integration in quantum physics and stochastic Langevin-turbulent partial differential equations. | ||
| 650 | 0 | |a Differential equations. |0 http://id.loc.gov/authorities/subjects/sh85037890 | |
| 650 | 0 | |a Functional analysis. |0 http://id.loc.gov/authorities/subjects/sh85052312 | |
| 650 | 0 | |a Mathematical physics. |0 http://id.loc.gov/authorities/subjects/sh85082129 | |
| 650 | 6 | |a Équations différentielles. | |
| 650 | 6 | |a Analyse fonctionnelle. | |
| 650 | 6 | |a Physique mathématique. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x General. |2 bisacsh | |
| 650 | 7 | |a Differential equations |2 fast | |
| 650 | 7 | |a Functional analysis |2 fast | |
| 650 | 7 | |a Mathematical physics |2 fast | |
| 758 | |i has work: |a Lecture notes in applied differential equations of mathematical physics (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGW6xfJhHPQy3HmT3RGwT3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Botelho, Luiz C.L. |t Lecture notes in applied differential equations of mathematical physics. |d Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2008 |w (DLC) 2009285117 |
| 856 | 1 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521209 |3 Volltext | |
| 856 | 1 | |l CBO01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521209 |3 Volltext | |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH24685781 | ||
| 938 | |a EBSCOhost |b EBSC |n 521209 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n cis25732086 | ||
| 938 | |a YBP Library Services |b YANK |n 9975189 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn820944533 |
|---|---|
| _version_ | 1813903595518558208 |
| adam_text | |
| any_adam_object | |
| author | Botelho, Luiz C. L. |
| author_facet | Botelho, Luiz C. L. |
| author_role | |
| author_sort | Botelho, Luiz C. L. |
| author_variant | l c l b lcl lclb |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QC20 |
| callnumber-raw | QC20.7.D5 |
| callnumber-search | QC20.7.D5 |
| callnumber-sort | QC 220.7 D5 |
| callnumber-subject | QC - Physics |
| collection | ZDB-4-EBA |
| contents | Ch. 1. Elementary aspects of potential theory in mathematical physics. 1.1. Introduction. 1.2. The Laplace differential operator and the Poisson-Dirichlet potential problem. 1.3. The Dirichlet problem in connected planar regions: a conformal transformation method for green functions in string theory. 1.4. Hilbert spaces methods in the Poisson problem. 1.5. The abstract formulation of the Poisson problem. 1.6. Potential theory for the wave equation in R[symbol] -- Kirchhoff potentials (spherical means). 1.7. The Dirichlet problem for the diffusion equation -- seminar exercises. 1.8. The potential theory in distributional spaces -- The Gelfand-Chilov method. Ch. 2. Scattering theory in non-relativistic one-body short-range quantum mechanics: Möller wave operators and asymptotic completeness. 2.1. The wave operators in one-body quantum mechanics asymptotic properties of states in the continuous spectra of the Enss Hamiltonian. 2.2. The Enss proof of the non-relativistic one-body quantum mechanical scattering -- ch. 3. On the Hilbert space integration method for the wave equation and some applications to wave physics. 3.1. Introduction. 3.2. The abstract spectral method -- the nondissipative case. 3.3. The abstract spectral method -- the dissipative case. 3.4. The wave equation "path-integral" propagator. 3.5. On the existence of wave-scattering operators. 3.6. Exponential stability in two-dimensional magneto-elasticity: a proof on a dissipative medium. 3.7. An abstract semilinear Klein Gordon wave equation -- existence and uniqueness. Ch. 4. Nonlinear diffusion and wave-damped propagation: weak solutions and statistical turbulence behavior. 4.1. Introduction. 4.2. The theorem for parabolic nonlinear diffusion. 4.3. The hyperbolic nonlinear damping. 4.4. A path-integral solution for the parabolic nonlinear diffusion. 4.5. Random anomalous diffusion, a semigroup approach -- ch. 5. Domains of Bosonic functional integrals and some applications to the mathematical physics of path-integrals and string theory. 5.1. Introduction. 5.2. The Euclidean Schwinger generating functional as a functional Fourier transform. 5.3. The support of functional measures -- the Minlos theorem. 5.4. Some rigorous quantum field path-integral in the analytical regularization scheme. 5.5. Remarks on the theory of integration of functionals on distributional spaces and Hilbert-Banach spaces. Ch. 6. Basic integral representations in mathematical analysis of Euclidean functional integrals. 6.1. On the Riesz-Markov theorem. 6.2. The L. Schwartz representation theorem on [symbol] (distribution theory). 6.3. Equivalence of Gaussian measures in Hilbert spaces and functional Jacobians. 6.4. On the weak Poisson problem in infinite dimension. 6.5. The path-integral triviality argument. 6.6. The loop space argument for the thirring model triviality -- ch. 7. Nonlinear diffusion in R[symbol] and Hilbert spaces: a path-integral study. 7.1. Introduction. 7.2. The nonlinear diffusion. 7.3. The linear diffusion in the space [symbol]. Ch. 8. On the Ergodic theorem. 8.1. Introduction. 8.2. On the detailed mathematical proof of the RAGE theorem. 8.3. On the Boltzmann Ergodic theorem in classical mechanics as a result of the RAGE theorem. 8.4. On the invariant Ergodic functional measure for some nonlinear wave equations. 8.5. An Ergodic theorem in Banach spaces and applications to stochastic-Langevin dynamical systems. 8.6. The existence and uniqueness results for some nonlinear wave motions in 2D -- ch. 9. Some comments on sampling of Ergodic process: an Ergodic theorem and turbulent pressure fluctuations. 9.1. Introduction. 9.2. A rigorous mathematical proof of the Ergodic theorem for wide-sense stationary stochastic process. 9.3. A sampling theorem for Ergodic process. 9.4. A model for the turbulent pressure fluctuations (random vibrations transmission). Ch. 10. Some studies on functional integrals pepresentations for fluid motion with random conditions. 10.1. Introduction. 10.2. The functional integral for initial fluid velocity random conditions. 10.3. An exactly soluble path-integral model for stochastic Beltrami fluxes and its string properties. 10.4. A complex trajectory path-integral representation or the Burger-Beltrami fluid flux -- ch. 11. The Atiyah-Singer index theorem: a heat kernel (PDE's) proof. |
| ctrlnum | (OCoLC)820944533 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>07586cam a2200625Ma 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn820944533</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20240705115654.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cn|||||||||</controlfield><controlfield tag="008">090522s2008 si a ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">LGG</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">LGG</subfield><subfield code="d">OCLCO</subfield><subfield code="d">N$T</subfield><subfield code="d">IDEBK</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AGLDB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">MERUC</subfield><subfield code="d">ZCU</subfield><subfield code="d">U3W</subfield><subfield code="d">STF</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">ICG</subfield><subfield code="d">INT</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">TKN</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">DKC</subfield><subfield code="d">AU@</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">M8D</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">1086427416</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789812814586</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9812814582</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9789812814579</subfield><subfield code="q">(hbk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9812814574</subfield><subfield code="q">(hbk.)</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)820944533</subfield><subfield code="z">(OCoLC)1086427416</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QC20.7.D5</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">007000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">515.35</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Botelho, Luiz C. L.</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Lecture notes in applied differential equations of mathematical physics /</subfield><subfield code="c">Luiz C.L. Botelho.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Singapore ;</subfield><subfield code="a">Hackensack, N.J. :</subfield><subfield code="b">World Scientific Pub. Co.,</subfield><subfield code="c">©2008.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Ch. 1. Elementary aspects of potential theory in mathematical physics. 1.1. Introduction. 1.2. The Laplace differential operator and the Poisson-Dirichlet potential problem. 1.3. The Dirichlet problem in connected planar regions: a conformal transformation method for green functions in string theory. 1.4. Hilbert spaces methods in the Poisson problem. 1.5. The abstract formulation of the Poisson problem. 1.6. Potential theory for the wave equation in R[symbol] -- Kirchhoff potentials (spherical means). 1.7. The Dirichlet problem for the diffusion equation -- seminar exercises. 1.8. The potential theory in distributional spaces -- The Gelfand-Chilov method.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Ch. 2. Scattering theory in non-relativistic one-body short-range quantum mechanics: Möller wave operators and asymptotic completeness. 2.1. The wave operators in one-body quantum mechanics asymptotic properties of states in the continuous spectra of the Enss Hamiltonian. 2.2. The Enss proof of the non-relativistic one-body quantum mechanical scattering -- ch. 3. On the Hilbert space integration method for the wave equation and some applications to wave physics. 3.1. Introduction. 3.2. The abstract spectral method -- the nondissipative case. 3.3. The abstract spectral method -- the dissipative case. 3.4. The wave equation "path-integral" propagator. 3.5. On the existence of wave-scattering operators. 3.6. Exponential stability in two-dimensional magneto-elasticity: a proof on a dissipative medium. 3.7. An abstract semilinear Klein Gordon wave equation -- existence and uniqueness.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Ch. 4. Nonlinear diffusion and wave-damped propagation: weak solutions and statistical turbulence behavior. 4.1. Introduction. 4.2. The theorem for parabolic nonlinear diffusion. 4.3. The hyperbolic nonlinear damping. 4.4. A path-integral solution for the parabolic nonlinear diffusion. 4.5. Random anomalous diffusion, a semigroup approach -- ch. 5. Domains of Bosonic functional integrals and some applications to the mathematical physics of path-integrals and string theory. 5.1. Introduction. 5.2. The Euclidean Schwinger generating functional as a functional Fourier transform. 5.3. The support of functional measures -- the Minlos theorem. 5.4. Some rigorous quantum field path-integral in the analytical regularization scheme. 5.5. Remarks on the theory of integration of functionals on distributional spaces and Hilbert-Banach spaces.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Ch. 6. Basic integral representations in mathematical analysis of Euclidean functional integrals. 6.1. On the Riesz-Markov theorem. 6.2. The L. Schwartz representation theorem on [symbol] (distribution theory). 6.3. Equivalence of Gaussian measures in Hilbert spaces and functional Jacobians. 6.4. On the weak Poisson problem in infinite dimension. 6.5. The path-integral triviality argument. 6.6. The loop space argument for the thirring model triviality -- ch. 7. Nonlinear diffusion in R[symbol] and Hilbert spaces: a path-integral study. 7.1. Introduction. 7.2. The nonlinear diffusion. 7.3. The linear diffusion in the space [symbol].</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Ch. 8. On the Ergodic theorem. 8.1. Introduction. 8.2. On the detailed mathematical proof of the RAGE theorem. 8.3. On the Boltzmann Ergodic theorem in classical mechanics as a result of the RAGE theorem. 8.4. On the invariant Ergodic functional measure for some nonlinear wave equations. 8.5. An Ergodic theorem in Banach spaces and applications to stochastic-Langevin dynamical systems. 8.6. The existence and uniqueness results for some nonlinear wave motions in 2D -- ch. 9. Some comments on sampling of Ergodic process: an Ergodic theorem and turbulent pressure fluctuations. 9.1. Introduction. 9.2. A rigorous mathematical proof of the Ergodic theorem for wide-sense stationary stochastic process. 9.3. A sampling theorem for Ergodic process. 9.4. A model for the turbulent pressure fluctuations (random vibrations transmission).</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Ch. 10. Some studies on functional integrals pepresentations for fluid motion with random conditions. 10.1. Introduction. 10.2. The functional integral for initial fluid velocity random conditions. 10.3. An exactly soluble path-integral model for stochastic Beltrami fluxes and its string properties. 10.4. A complex trajectory path-integral representation or the Burger-Beltrami fluid flux -- ch. 11. The Atiyah-Singer index theorem: a heat kernel (PDE's) proof.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Functional analysis is a well-established powerful method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and statistical turbulence. This book presents a unique, modern treatment of solutions to fractional random differential equations in mathematical physics. It follows an analytic approach in applied functional analysis for functional integration in quantum physics and stochastic Langevin-turbulent partial differential equations.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Differential equations.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85037890</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Functional analysis.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85052312</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Mathematical physics.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85082129</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Équations différentielles.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Analyse fonctionnelle.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Physique mathématique.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Differential Equations</subfield><subfield code="x">General.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Differential equations</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Functional analysis</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Mathematical physics</subfield><subfield code="2">fast</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Lecture notes in applied differential equations of mathematical physics (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCGW6xfJhHPQy3HmT3RGwT3</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Botelho, Luiz C.L.</subfield><subfield code="t">Lecture notes in applied differential equations of mathematical physics.</subfield><subfield code="d">Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2008</subfield><subfield code="w">(DLC) 2009285117</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521209</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">CBO01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521209</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH24685781</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">521209</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">cis25732086</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">9975189</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn820944533 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:21:10Z |
| institution | BVB |
| isbn | 9789812814586 9812814582 |
| language | English |
| oclc_num | 820944533 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource |
| psigel | ZDB-4-EBA |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | World Scientific Pub. Co., |
| record_format | marc |
| spelling | Botelho, Luiz C. L. Lecture notes in applied differential equations of mathematical physics / Luiz C.L. Botelho. Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2008. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references and index. Ch. 1. Elementary aspects of potential theory in mathematical physics. 1.1. Introduction. 1.2. The Laplace differential operator and the Poisson-Dirichlet potential problem. 1.3. The Dirichlet problem in connected planar regions: a conformal transformation method for green functions in string theory. 1.4. Hilbert spaces methods in the Poisson problem. 1.5. The abstract formulation of the Poisson problem. 1.6. Potential theory for the wave equation in R[symbol] -- Kirchhoff potentials (spherical means). 1.7. The Dirichlet problem for the diffusion equation -- seminar exercises. 1.8. The potential theory in distributional spaces -- The Gelfand-Chilov method. Ch. 2. Scattering theory in non-relativistic one-body short-range quantum mechanics: Möller wave operators and asymptotic completeness. 2.1. The wave operators in one-body quantum mechanics asymptotic properties of states in the continuous spectra of the Enss Hamiltonian. 2.2. The Enss proof of the non-relativistic one-body quantum mechanical scattering -- ch. 3. On the Hilbert space integration method for the wave equation and some applications to wave physics. 3.1. Introduction. 3.2. The abstract spectral method -- the nondissipative case. 3.3. The abstract spectral method -- the dissipative case. 3.4. The wave equation "path-integral" propagator. 3.5. On the existence of wave-scattering operators. 3.6. Exponential stability in two-dimensional magneto-elasticity: a proof on a dissipative medium. 3.7. An abstract semilinear Klein Gordon wave equation -- existence and uniqueness. Ch. 4. Nonlinear diffusion and wave-damped propagation: weak solutions and statistical turbulence behavior. 4.1. Introduction. 4.2. The theorem for parabolic nonlinear diffusion. 4.3. The hyperbolic nonlinear damping. 4.4. A path-integral solution for the parabolic nonlinear diffusion. 4.5. Random anomalous diffusion, a semigroup approach -- ch. 5. Domains of Bosonic functional integrals and some applications to the mathematical physics of path-integrals and string theory. 5.1. Introduction. 5.2. The Euclidean Schwinger generating functional as a functional Fourier transform. 5.3. The support of functional measures -- the Minlos theorem. 5.4. Some rigorous quantum field path-integral in the analytical regularization scheme. 5.5. Remarks on the theory of integration of functionals on distributional spaces and Hilbert-Banach spaces. Ch. 6. Basic integral representations in mathematical analysis of Euclidean functional integrals. 6.1. On the Riesz-Markov theorem. 6.2. The L. Schwartz representation theorem on [symbol] (distribution theory). 6.3. Equivalence of Gaussian measures in Hilbert spaces and functional Jacobians. 6.4. On the weak Poisson problem in infinite dimension. 6.5. The path-integral triviality argument. 6.6. The loop space argument for the thirring model triviality -- ch. 7. Nonlinear diffusion in R[symbol] and Hilbert spaces: a path-integral study. 7.1. Introduction. 7.2. The nonlinear diffusion. 7.3. The linear diffusion in the space [symbol]. Ch. 8. On the Ergodic theorem. 8.1. Introduction. 8.2. On the detailed mathematical proof of the RAGE theorem. 8.3. On the Boltzmann Ergodic theorem in classical mechanics as a result of the RAGE theorem. 8.4. On the invariant Ergodic functional measure for some nonlinear wave equations. 8.5. An Ergodic theorem in Banach spaces and applications to stochastic-Langevin dynamical systems. 8.6. The existence and uniqueness results for some nonlinear wave motions in 2D -- ch. 9. Some comments on sampling of Ergodic process: an Ergodic theorem and turbulent pressure fluctuations. 9.1. Introduction. 9.2. A rigorous mathematical proof of the Ergodic theorem for wide-sense stationary stochastic process. 9.3. A sampling theorem for Ergodic process. 9.4. A model for the turbulent pressure fluctuations (random vibrations transmission). Ch. 10. Some studies on functional integrals pepresentations for fluid motion with random conditions. 10.1. Introduction. 10.2. The functional integral for initial fluid velocity random conditions. 10.3. An exactly soluble path-integral model for stochastic Beltrami fluxes and its string properties. 10.4. A complex trajectory path-integral representation or the Burger-Beltrami fluid flux -- ch. 11. The Atiyah-Singer index theorem: a heat kernel (PDE's) proof. Functional analysis is a well-established powerful method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and statistical turbulence. This book presents a unique, modern treatment of solutions to fractional random differential equations in mathematical physics. It follows an analytic approach in applied functional analysis for functional integration in quantum physics and stochastic Langevin-turbulent partial differential equations. Differential equations. http://id.loc.gov/authorities/subjects/sh85037890 Functional analysis. http://id.loc.gov/authorities/subjects/sh85052312 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Équations différentielles. Analyse fonctionnelle. Physique mathématique. MATHEMATICS Differential Equations General. bisacsh Differential equations fast Functional analysis fast Mathematical physics fast has work: Lecture notes in applied differential equations of mathematical physics (Text) https://id.oclc.org/worldcat/entity/E39PCGW6xfJhHPQy3HmT3RGwT3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Botelho, Luiz C.L. Lecture notes in applied differential equations of mathematical physics. Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2008 (DLC) 2009285117 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521209 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521209 Volltext |
| spellingShingle | Botelho, Luiz C. L. Lecture notes in applied differential equations of mathematical physics / Ch. 1. Elementary aspects of potential theory in mathematical physics. 1.1. Introduction. 1.2. The Laplace differential operator and the Poisson-Dirichlet potential problem. 1.3. The Dirichlet problem in connected planar regions: a conformal transformation method for green functions in string theory. 1.4. Hilbert spaces methods in the Poisson problem. 1.5. The abstract formulation of the Poisson problem. 1.6. Potential theory for the wave equation in R[symbol] -- Kirchhoff potentials (spherical means). 1.7. The Dirichlet problem for the diffusion equation -- seminar exercises. 1.8. The potential theory in distributional spaces -- The Gelfand-Chilov method. Ch. 2. Scattering theory in non-relativistic one-body short-range quantum mechanics: Möller wave operators and asymptotic completeness. 2.1. The wave operators in one-body quantum mechanics asymptotic properties of states in the continuous spectra of the Enss Hamiltonian. 2.2. The Enss proof of the non-relativistic one-body quantum mechanical scattering -- ch. 3. On the Hilbert space integration method for the wave equation and some applications to wave physics. 3.1. Introduction. 3.2. The abstract spectral method -- the nondissipative case. 3.3. The abstract spectral method -- the dissipative case. 3.4. The wave equation "path-integral" propagator. 3.5. On the existence of wave-scattering operators. 3.6. Exponential stability in two-dimensional magneto-elasticity: a proof on a dissipative medium. 3.7. An abstract semilinear Klein Gordon wave equation -- existence and uniqueness. Ch. 4. Nonlinear diffusion and wave-damped propagation: weak solutions and statistical turbulence behavior. 4.1. Introduction. 4.2. The theorem for parabolic nonlinear diffusion. 4.3. The hyperbolic nonlinear damping. 4.4. A path-integral solution for the parabolic nonlinear diffusion. 4.5. Random anomalous diffusion, a semigroup approach -- ch. 5. Domains of Bosonic functional integrals and some applications to the mathematical physics of path-integrals and string theory. 5.1. Introduction. 5.2. The Euclidean Schwinger generating functional as a functional Fourier transform. 5.3. The support of functional measures -- the Minlos theorem. 5.4. Some rigorous quantum field path-integral in the analytical regularization scheme. 5.5. Remarks on the theory of integration of functionals on distributional spaces and Hilbert-Banach spaces. Ch. 6. Basic integral representations in mathematical analysis of Euclidean functional integrals. 6.1. On the Riesz-Markov theorem. 6.2. The L. Schwartz representation theorem on [symbol] (distribution theory). 6.3. Equivalence of Gaussian measures in Hilbert spaces and functional Jacobians. 6.4. On the weak Poisson problem in infinite dimension. 6.5. The path-integral triviality argument. 6.6. The loop space argument for the thirring model triviality -- ch. 7. Nonlinear diffusion in R[symbol] and Hilbert spaces: a path-integral study. 7.1. Introduction. 7.2. The nonlinear diffusion. 7.3. The linear diffusion in the space [symbol]. Ch. 8. On the Ergodic theorem. 8.1. Introduction. 8.2. On the detailed mathematical proof of the RAGE theorem. 8.3. On the Boltzmann Ergodic theorem in classical mechanics as a result of the RAGE theorem. 8.4. On the invariant Ergodic functional measure for some nonlinear wave equations. 8.5. An Ergodic theorem in Banach spaces and applications to stochastic-Langevin dynamical systems. 8.6. The existence and uniqueness results for some nonlinear wave motions in 2D -- ch. 9. Some comments on sampling of Ergodic process: an Ergodic theorem and turbulent pressure fluctuations. 9.1. Introduction. 9.2. A rigorous mathematical proof of the Ergodic theorem for wide-sense stationary stochastic process. 9.3. A sampling theorem for Ergodic process. 9.4. A model for the turbulent pressure fluctuations (random vibrations transmission). Ch. 10. Some studies on functional integrals pepresentations for fluid motion with random conditions. 10.1. Introduction. 10.2. The functional integral for initial fluid velocity random conditions. 10.3. An exactly soluble path-integral model for stochastic Beltrami fluxes and its string properties. 10.4. A complex trajectory path-integral representation or the Burger-Beltrami fluid flux -- ch. 11. The Atiyah-Singer index theorem: a heat kernel (PDE's) proof. Differential equations. http://id.loc.gov/authorities/subjects/sh85037890 Functional analysis. http://id.loc.gov/authorities/subjects/sh85052312 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Équations différentielles. Analyse fonctionnelle. Physique mathématique. MATHEMATICS Differential Equations General. bisacsh Differential equations fast Functional analysis fast Mathematical physics fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85037890 http://id.loc.gov/authorities/subjects/sh85052312 http://id.loc.gov/authorities/subjects/sh85082129 |
| title | Lecture notes in applied differential equations of mathematical physics / |
| title_auth | Lecture notes in applied differential equations of mathematical physics / |
| title_exact_search | Lecture notes in applied differential equations of mathematical physics / |
| title_full | Lecture notes in applied differential equations of mathematical physics / Luiz C.L. Botelho. |
| title_fullStr | Lecture notes in applied differential equations of mathematical physics / Luiz C.L. Botelho. |
| title_full_unstemmed | Lecture notes in applied differential equations of mathematical physics / Luiz C.L. Botelho. |
| title_short | Lecture notes in applied differential equations of mathematical physics / |
| title_sort | lecture notes in applied differential equations of mathematical physics |
| topic | Differential equations. http://id.loc.gov/authorities/subjects/sh85037890 Functional analysis. http://id.loc.gov/authorities/subjects/sh85052312 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Équations différentielles. Analyse fonctionnelle. Physique mathématique. MATHEMATICS Differential Equations General. bisacsh Differential equations fast Functional analysis fast Mathematical physics fast |
| topic_facet | Differential equations. Functional analysis. Mathematical physics. Équations différentielles. Analyse fonctionnelle. Physique mathématique. MATHEMATICS Differential Equations General. Differential equations Functional analysis Mathematical physics |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521209 |
| work_keys_str_mv | AT botelholuizcl lecturenotesinapplieddifferentialequationsofmathematicalphysics |