Stability, instability, and direct integrals:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
1999
|
| Schriftenreihe: | Chapman & Hall CRC research notes in mathematics series
402 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 346 S. |
| ISBN: | 084930685X |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV012656432 | ||
| 003 | DE-604 | ||
| 005 | 20021202 | ||
| 007 | t | ||
| 008 | 990712s1999 |||| 00||| eng d | ||
| 020 | |a 084930685X |9 0-8493-0685-X | ||
| 035 | |a (OCoLC)35229171 | ||
| 035 | |a (DE-599)BVBBV012656432 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-703 |a DE-12 |a DE-824 | ||
| 050 | 0 | |a QA377 | |
| 082 | 0 | |a 515/.353 |2 20 | |
| 084 | |a SI 880 |0 (DE-625)143209: |2 rvk | ||
| 084 | |a SK 600 |0 (DE-625)143248: |2 rvk | ||
| 100 | 1 | |a Scarpellini, Bruno |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stability, instability, and direct integrals |c Bruno Scarpellini |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 1999 | |
| 300 | |a 346 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Chapman & Hall CRC research notes in mathematics series |v 402 | |
| 650 | 4 | |a Equation Boussinesq | |
| 650 | 4 | |a Equation Navier-Stokes | |
| 650 | 4 | |a Instabilité | |
| 650 | 4 | |a Instabilité linéarisée | |
| 650 | 4 | |a Intégrale directe | |
| 650 | 7 | |a Parabolische differentiaalvergelijkingen |2 gtt | |
| 650 | 4 | |a Point fixe | |
| 650 | 4 | |a Réaction-diffusion | |
| 650 | 4 | |a Stabilité | |
| 650 | 4 | |a Théorie spectrale | |
| 650 | 4 | |a Trace série Fourier | |
| 650 | 7 | |a Équations différentielles paraboliques - Analyse numérique |2 ram | |
| 650 | 4 | |a Differential equations, Parabolic |x Numerical solutions | |
| 650 | 4 | |a Lyapunov stability | |
| 650 | 0 | 7 | |a Direktes Integral |0 (DE-588)4554581-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ljapunov-Stabilitätstheorie |0 (DE-588)4167992-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare partielle Differentialgleichung |0 (DE-588)4128900-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare partielle Differentialgleichung |0 (DE-588)4128900-6 |D s |
| 689 | 0 | 1 | |a Ljapunov-Stabilitätstheorie |0 (DE-588)4167992-1 |D s |
| 689 | 0 | 2 | |a Direktes Integral |0 (DE-588)4554581-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Chapman & Hall CRC research notes in mathematics series |v 402 |w (DE-604)BV012456897 |9 402 | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008598799&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-008598799 | ||
Datensatz im Suchindex
| _version_ | 1804127313571348480 |
|---|---|
| adam_text | BRUNO SCARPELLINI MATHEMATISCHES INSTITUT DER UNIVERSITAET BASEL
STABILITY, INSTABILITY, AND DIRECT INTEGRALS CHAPMAN & HALL/CRC BOCA
RATON LONDON NEW YORK WASHINGTON, D.C. CONTENTS PREFACE NOTATIONS AND
PRELIMINARIES INTRODUCTION CHAPTER 1. REACTION-DIFFUSION SYSTEMS ON AN
INFINITE PLATE 1 1.1. REACTION-DIFFUSION SYSTEMS ON AN INFINITE PLATE 1
1.2. THE LAPLACIAN ON AN INFINITE PLATE. 2 CHAPTER 2. FLOQUET-PERIODIC
FUNCTIONS 9 2.1. 0-PERIODIC FUNCTIONS 9 2.2. FOURIER SERIES 12 2.3. THE
6-PERIODIC LAPLACIAN 18 2.4. THE PERIODIC CASE 22 CHAPTER 3. DIRECT
INTEGRALS 25 3.1. DIRECT INTEGRALS OF HUBERT SPACES 25 3.2. DIRECT
INTEGRALS OF OPERATORS 34 CHAPTER 4. SPECTRAL CONSIDERATIONS 41 4.1.
RELATIONS BETWEEN MEASURE AND SPECTRA 41 4.2. HOLOMORPHIC FAMILIES OF
OPERATORS 45 4.3. PROOF OF LEMMA 4.2 51 4.4. COMMENTS 62 CHAPTER 5.
NAVIER-STOKES ON AN INFINITE PLATE 65 5.1. NAVIER-STOKES ON AN INFINITE
PLATE 66 5.2. THE STOKES OPERATOR ON THE INFINITE PLATE 67 5.3. FOURIER
EXPANSIONS 72 5.4. THE PROJECTION OPERATOR P 81 CHAPTER 6. THE
FLOQUET-PERIODIC STOKES OPERATOR 93 6.1. PARITY CONSIDERATIONS 94 6.2.
TRACES EXPRESSED IN TERMS OF FOURIER SERIES 95 6.3. THE 0-PERIODIC
STOKES OPERATOR 101 6.4. COMPUTATIONAL ASPECTS 106 6.5. SOME AUXILIARY
LEMMAS 113 6.6. THE REGULARITY PROOF 122 6.7. THE PROOF OF THEOREM 6.2
(A) 128 6.8. DISCUSSION OF THE REGULARITY PROOF 135 6.9. SOME
CONSEQUENCES OF THE REGULARITY PROOF 139 CHAPTER 7. THE 6-PERIODIC
PROJECTION OPERATOR 143 7.1. A DIFFERENT DEFINITION OF E& 143 7.2. THE
6-PERIODIC NEUMANN PROBLEM 146 7.3. THE 0-PERIODIC PROJECTION OPERATOR
150 CHAPTER 8. STOKES OPERATOR, PRESSURE, AND DIRECT INTEGRALS 153 8.1.
PREPARATORY STEPS 153 8.2. PROOF OF THEOREM 8.1 155 8.3. PROOF OF
THEOREM 8.2 158 8.4. PARITY RECONSIDERED 165 CHAPTER 9. SPECTRAL THEORY
AND DIRECT INTEGRALS 169 9.1. SOME HOLOMORPHIC FAMILIES OF OPERATORS 169
9.2. FAMILIES OF RESOLVENTS 181 9.3. LOCAL SPECTRAL RELATIONS 183 9.4.
THE CORNERS: PRELIMINARY REMARKS 190 9.5. THE CORNERS AND THEIR
INFLUENCE ON THE SPECTRUM 194 9.6. RELATIONSHIP WITH THE PERIODIC
SPECTRUM 216 CHAPTER 10. THE PRINCIPLE OF LINEARIZED INSTABILITY 221
10.1. REMARKS ON THE PRINCIPLE OF LINEARIZED INSTABILITY 222 10.2. REAL
ELEMENTS IN THE SPACE OF DIRECT INTEGRALS 226 10.3. A TOPOLOGICAL
INTERPRETATION 233 10.4. CONSTRUCTION OF A FAMILY OF PROJECTION
OPERATORS 247 10.5. DIRECT INTEGRAL REPRESENTATION OF A PROJECTION
OPERATOR 259 10.6. REMARKS 281 CHAPTER 11. THE PRINCIPLE OF LINEARIZED
INSTABILITY: NONLINEAR PART 283 11.1. THE NONLINEAR TERMS 283 11.2.
FURTHER REMARKS ON FRACTIONAL POWERS 295 11.3. FIXED POINTS OF AN
INTEGRAL EQUATION 300 11.4. INSTABILITY: PROOF OF THEOREM 10.2 312
11.5. INSTABILITY VIA COMPLEX PROJECTION OPERATORS 319 11.6. FURTHER
REMARKS 322 CHAPTER 12. THE BOUSSINESQ EQUATIONS 323 12.1. THE
BOUSSINESQ EQUATIONS 324 12.2. REMARKS ON THE INFINITE PLATE 330 12.3.
REMARKS ON THE 6-PERIODIC SETTING 330 12.4. REMARKS ON DIRECT INTEGRALS
331 12.5. REMARKS ON SPECTRAL THEORY 333 12.6. REMARKS ON THE PRINCIPLE
OF LINEARIZED INSTABILITY 338 BIBLIOGRAPHY 341 INDEX 345
|
| any_adam_object | 1 |
| author | Scarpellini, Bruno |
| author_facet | Scarpellini, Bruno |
| author_role | aut |
| author_sort | Scarpellini, Bruno |
| author_variant | b s bs |
| building | Verbundindex |
| bvnumber | BV012656432 |
| callnumber-first | Q - Science |
| callnumber-label | QA377 |
| callnumber-raw | QA377 |
| callnumber-search | QA377 |
| callnumber-sort | QA 3377 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 880 SK 600 |
| ctrlnum | (OCoLC)35229171 (DE-599)BVBBV012656432 |
| dewey-full | 515/.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 |
| dewey-search | 515/.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02360nam a2200589 cb4500</leader><controlfield tag="001">BV012656432</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20021202 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">990712s1999 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">084930685X</subfield><subfield code="9">0-8493-0685-X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)35229171</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV012656432</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-824</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA377</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.353</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 880</subfield><subfield code="0">(DE-625)143209:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 600</subfield><subfield code="0">(DE-625)143248:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Scarpellini, Bruno</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Stability, instability, and direct integrals</subfield><subfield code="c">Bruno Scarpellini</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boca Raton [u.a.]</subfield><subfield code="b">Chapman & Hall/CRC</subfield><subfield code="c">1999</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">346 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Chapman & Hall CRC research notes in mathematics series</subfield><subfield code="v">402</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Equation Boussinesq</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Equation Navier-Stokes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Instabilité</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Instabilité linéarisée</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Intégrale directe</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Parabolische differentiaalvergelijkingen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Point fixe</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Réaction-diffusion</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stabilité</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Théorie spectrale</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Trace série Fourier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Équations différentielles paraboliques - Analyse numérique</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, Parabolic</subfield><subfield code="x">Numerical solutions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lyapunov stability</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Direktes Integral</subfield><subfield code="0">(DE-588)4554581-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Ljapunov-Stabilitätstheorie</subfield><subfield code="0">(DE-588)4167992-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4128900-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtlineare partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4128900-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Ljapunov-Stabilitätstheorie</subfield><subfield code="0">(DE-588)4167992-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Direktes Integral</subfield><subfield code="0">(DE-588)4554581-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Chapman & Hall CRC research notes in mathematics series</subfield><subfield code="v">402</subfield><subfield code="w">(DE-604)BV012456897</subfield><subfield code="9">402</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008598799&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-008598799</subfield></datafield></record></collection> |
| id | DE-604.BV012656432 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:31:22Z |
| institution | BVB |
| isbn | 084930685X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008598799 |
| oclc_num | 35229171 |
| open_access_boolean | |
| owner | DE-703 DE-12 DE-824 |
| owner_facet | DE-703 DE-12 DE-824 |
| physical | 346 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Chapman & Hall CRC research notes in mathematics series |
| series2 | Chapman & Hall CRC research notes in mathematics series |
| spelling | Scarpellini, Bruno Verfasser aut Stability, instability, and direct integrals Bruno Scarpellini Boca Raton [u.a.] Chapman & Hall/CRC 1999 346 S. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall CRC research notes in mathematics series 402 Equation Boussinesq Equation Navier-Stokes Instabilité Instabilité linéarisée Intégrale directe Parabolische differentiaalvergelijkingen gtt Point fixe Réaction-diffusion Stabilité Théorie spectrale Trace série Fourier Équations différentielles paraboliques - Analyse numérique ram Differential equations, Parabolic Numerical solutions Lyapunov stability Direktes Integral (DE-588)4554581-9 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s Direktes Integral (DE-588)4554581-9 s DE-604 Chapman & Hall CRC research notes in mathematics series 402 (DE-604)BV012456897 402 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008598799&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Scarpellini, Bruno Stability, instability, and direct integrals Chapman & Hall CRC research notes in mathematics series Equation Boussinesq Equation Navier-Stokes Instabilité Instabilité linéarisée Intégrale directe Parabolische differentiaalvergelijkingen gtt Point fixe Réaction-diffusion Stabilité Théorie spectrale Trace série Fourier Équations différentielles paraboliques - Analyse numérique ram Differential equations, Parabolic Numerical solutions Lyapunov stability Direktes Integral (DE-588)4554581-9 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4554581-9 (DE-588)4167992-1 (DE-588)4128900-6 |
| title | Stability, instability, and direct integrals |
| title_auth | Stability, instability, and direct integrals |
| title_exact_search | Stability, instability, and direct integrals |
| title_full | Stability, instability, and direct integrals Bruno Scarpellini |
| title_fullStr | Stability, instability, and direct integrals Bruno Scarpellini |
| title_full_unstemmed | Stability, instability, and direct integrals Bruno Scarpellini |
| title_short | Stability, instability, and direct integrals |
| title_sort | stability instability and direct integrals |
| topic | Equation Boussinesq Equation Navier-Stokes Instabilité Instabilité linéarisée Intégrale directe Parabolische differentiaalvergelijkingen gtt Point fixe Réaction-diffusion Stabilité Théorie spectrale Trace série Fourier Équations différentielles paraboliques - Analyse numérique ram Differential equations, Parabolic Numerical solutions Lyapunov stability Direktes Integral (DE-588)4554581-9 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Equation Boussinesq Equation Navier-Stokes Instabilité Instabilité linéarisée Intégrale directe Parabolische differentiaalvergelijkingen Point fixe Réaction-diffusion Stabilité Théorie spectrale Trace série Fourier Équations différentielles paraboliques - Analyse numérique Differential equations, Parabolic Numerical solutions Lyapunov stability Direktes Integral Ljapunov-Stabilitätstheorie Nichtlineare partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008598799&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV012456897 |
| work_keys_str_mv | AT scarpellinibruno stabilityinstabilityanddirectintegrals |