Non-self-adjoint boundary eigenvalue problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
North-Holland
2003
|
| Ausgabe: | 1st ed |
| Schriftenreihe: | North-Holland mathematics studies
192 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and <IT>n</IT>-th order ordinary differential equations. In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every <IT>n</IT>-th order differential equation is equivalent to a first order system, the main techniques are developed for systems. Asymptotic fundamental systems are derived for a large class of systems of differential equations. Together with boundary conditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10. The contour integral method and estimates of the resolvent are used to prove expansion theorems. For Stone regular problems, not all functions are expandable, and again relatively easy verifiable conditions are given, in terms of auxiliary boundary conditions, for functions to be expandable. Chapter 10 deals exclusively with applications; in nine sections, various concrete problems such as the Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated. Key features: & bull; Expansion Theorems for Ordinary Differential Equations & bull; Discusses Applications to Problems from Physics and Engineering & bull; Thorough Investigation of Asymptotic Fundamental Matrices and Systems & bull; Provides a Comprehensive Treatment & bull; Uses the Contour Integral Method & bull; Represents the Problems as Bounded Operators & bull; Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions Includes bibliographical references (p. 475-495) and index |
| Beschreibung: | 1 Online-Ressource (xviii, 500 p.) |
| ISBN: | 9780444514479 0444514473 |
Internformat
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| 245 | 1 | 0 | |a Non-self-adjoint boundary eigenvalue problems |c Reinhard Mennicken and Manfred Möller |
| 250 | |a 1st ed | ||
| 264 | 1 | |a Amsterdam |b North-Holland |c 2003 | |
| 300 | |a 1 Online-Ressource (xviii, 500 p.) | ||
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| 490 | 0 | |a North-Holland mathematics studies |v 192 | |
| 500 | |a This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and <IT>n</IT>-th order ordinary differential equations. In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every <IT>n</IT>-th order differential equation is equivalent to a first order system, the main techniques are developed for systems. Asymptotic fundamental systems are derived for a large class of systems of differential equations. Together with boundary conditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. | ||
| 500 | |a An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10. The contour integral method and estimates of the resolvent are used to prove expansion theorems. For Stone regular problems, not all functions are expandable, and again relatively easy verifiable conditions are given, in terms of auxiliary boundary conditions, for functions to be expandable. Chapter 10 deals exclusively with applications; in nine sections, various concrete problems such as the Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated. | ||
| 500 | |a Key features: & bull; Expansion Theorems for Ordinary Differential Equations & bull; Discusses Applications to Problems from Physics and Engineering & bull; Thorough Investigation of Asymptotic Fundamental Matrices and Systems & bull; Provides a Comprehensive Treatment & bull; Uses the Contour Integral Method & bull; Represents the Problems as Bounded Operators & bull; Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions | ||
| 500 | |a Includes bibliographical references (p. 475-495) and index | ||
| 650 | 4 | |a Problèmes aux limites | |
| 650 | 4 | |a Opérateurs non auto-adjoints | |
| 650 | 4 | |a Valeurs propres | |
| 650 | 4 | |a Équations différentielles | |
| 650 | 7 | |a Problemas de contorno |2 larpcal | |
| 650 | 7 | |a Operadores |2 larpcal | |
| 650 | 7 | |a Espaços de sobolev |2 larpcal | |
| 650 | 7 | |a Equações diferenciais |2 larpcal | |
| 650 | 7 | |a Boundary value problems |2 fast | |
| 650 | 7 | |a Differential equations |2 fast | |
| 650 | 7 | |a Eigenvalues |2 fast | |
| 650 | 7 | |a Nonselfadjoint operators |2 fast | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Nonselfadjoint operators | |
| 650 | 4 | |a Eigenvalues | |
| 650 | 4 | |a Differential equations | |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Randwertproblem |0 (DE-588)4048395-2 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Möller, Manfred |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u http://www.sciencedirect.com/science/book/9780444514479 |x Verlag |3 Volltext |
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Datensatz im Suchindex
| _version_ | 1804152913650515968 |
|---|---|
| any_adam_object | |
| author | Mennicken, Reinhard |
| author_facet | Mennicken, Reinhard |
| author_role | aut |
| author_sort | Mennicken, Reinhard |
| author_variant | r m rm |
| building | Verbundindex |
| bvnumber | BV042317340 |
| collection | ZDB-33-ESD ZDB-33-EBS |
| ctrlnum | (ZDB-33-EBS)ocn162579804 (OCoLC)162579804 (DE-599)BVBBV042317340 |
| 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 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1st ed |
| format | Electronic eBook |
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| id | DE-604.BV042317340 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:18:16Z |
| institution | BVB |
| isbn | 9780444514479 0444514473 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027754330 |
| oclc_num | 162579804 |
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| owner_facet | DE-1046 |
| physical | 1 Online-Ressource (xviii, 500 p.) |
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| publishDate | 2003 |
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| publisher | North-Holland |
| record_format | marc |
| series2 | North-Holland mathematics studies |
| spelling | Mennicken, Reinhard Verfasser aut Non-self-adjoint boundary eigenvalue problems Reinhard Mennicken and Manfred Möller 1st ed Amsterdam North-Holland 2003 1 Online-Ressource (xviii, 500 p.) txt rdacontent c rdamedia cr rdacarrier North-Holland mathematics studies 192 This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and <IT>n</IT>-th order ordinary differential equations. In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every <IT>n</IT>-th order differential equation is equivalent to a first order system, the main techniques are developed for systems. Asymptotic fundamental systems are derived for a large class of systems of differential equations. Together with boundary conditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10. The contour integral method and estimates of the resolvent are used to prove expansion theorems. For Stone regular problems, not all functions are expandable, and again relatively easy verifiable conditions are given, in terms of auxiliary boundary conditions, for functions to be expandable. Chapter 10 deals exclusively with applications; in nine sections, various concrete problems such as the Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated. Key features: & bull; Expansion Theorems for Ordinary Differential Equations & bull; Discusses Applications to Problems from Physics and Engineering & bull; Thorough Investigation of Asymptotic Fundamental Matrices and Systems & bull; Provides a Comprehensive Treatment & bull; Uses the Contour Integral Method & bull; Represents the Problems as Bounded Operators & bull; Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions Includes bibliographical references (p. 475-495) and index Problèmes aux limites Opérateurs non auto-adjoints Valeurs propres Équations différentielles Problemas de contorno larpcal Operadores larpcal Espaços de sobolev larpcal Equações diferenciais larpcal Boundary value problems fast Differential equations fast Eigenvalues fast Nonselfadjoint operators fast Boundary value problems Nonselfadjoint operators Eigenvalues Differential equations Randwertproblem (DE-588)4048395-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 s 1\p DE-604 Möller, Manfred Sonstige oth http://www.sciencedirect.com/science/book/9780444514479 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mennicken, Reinhard Non-self-adjoint boundary eigenvalue problems Problèmes aux limites Opérateurs non auto-adjoints Valeurs propres Équations différentielles Problemas de contorno larpcal Operadores larpcal Espaços de sobolev larpcal Equações diferenciais larpcal Boundary value problems fast Differential equations fast Eigenvalues fast Nonselfadjoint operators fast Boundary value problems Nonselfadjoint operators Eigenvalues Differential equations Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4048395-2 |
| title | Non-self-adjoint boundary eigenvalue problems |
| title_auth | Non-self-adjoint boundary eigenvalue problems |
| title_exact_search | Non-self-adjoint boundary eigenvalue problems |
| title_full | Non-self-adjoint boundary eigenvalue problems Reinhard Mennicken and Manfred Möller |
| title_fullStr | Non-self-adjoint boundary eigenvalue problems Reinhard Mennicken and Manfred Möller |
| title_full_unstemmed | Non-self-adjoint boundary eigenvalue problems Reinhard Mennicken and Manfred Möller |
| title_short | Non-self-adjoint boundary eigenvalue problems |
| title_sort | non self adjoint boundary eigenvalue problems |
| topic | Problèmes aux limites Opérateurs non auto-adjoints Valeurs propres Équations différentielles Problemas de contorno larpcal Operadores larpcal Espaços de sobolev larpcal Equações diferenciais larpcal Boundary value problems fast Differential equations fast Eigenvalues fast Nonselfadjoint operators fast Boundary value problems Nonselfadjoint operators Eigenvalues Differential equations Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Problèmes aux limites Opérateurs non auto-adjoints Valeurs propres Équations différentielles Problemas de contorno Operadores Espaços de sobolev Equações diferenciais Boundary value problems Differential equations Eigenvalues Nonselfadjoint operators Randwertproblem |
| url | http://www.sciencedirect.com/science/book/9780444514479 |
| work_keys_str_mv | AT mennickenreinhard nonselfadjointboundaryeigenvalueproblems AT mollermanfred nonselfadjointboundaryeigenvalueproblems |