Nonlinear Spectral Theory / / Jürgen Appell, Espedito De Pascale, Alfonso Vignoli.
Aufgrund der herausragenden Bedeutung der Spektraltheorie linearer Operatoren in vielen Bereichen der Mathematik und Physik ist es nicht verwunderlich, dass verschiedene Versuche unternommen wurden, Spektren auch für nichtlineare Operatoren zu definieren und zu untersuchen. Dieses Buch bietet eine u...
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Appell, Jürgen, author. aut http://id.loc.gov/vocabulary/relators/aut Nonlinear Spectral Theory / Jürgen Appell, Espedito De Pascale, Alfonso Vignoli. Berlin ; Boston : De Gruyter, [2008] ©2004 1 online resource (408 p.) : Num. tab. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Series in Nonlinear Analysis and Applications , 0941-813X ; 10 Frontmatter -- Contents -- Introduction -- Chapter 1. Spectra of Bounded Linear -- Operators -- Chapter 2. Some Characteristics of Nonlinear -- Operators -- Chapter 3. Invertibility of Nonlinear -- Operators -- Chapter 4. The Rhodius and Neuberger -- Spectra -- Chapter 5. The Kachurovskij and Dörfner -- Spectra -- Chapter 6. The Furi–Martelli–Vignoli -- Spectrum -- Chapter 7. The Feng Spectrum -- Chapter 8. The Väth Phantom -- Chapter 9. Other Spectra -- Chapter 10. Nonlinear Eigenvalue Problems -- Chapter 11. Numerical Ranges of Nonlinear -- Operators -- Chapter 12. Some Applications -- Backmatter restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Aufgrund der herausragenden Bedeutung der Spektraltheorie linearer Operatoren in vielen Bereichen der Mathematik und Physik ist es nicht verwunderlich, dass verschiedene Versuche unternommen wurden, Spektren auch für nichtlineare Operatoren zu definieren und zu untersuchen. Dieses Buch bietet eine umfassende und in sich abgeschlossene Behandlung der Theorie, Methoden und Anwendungen der nichtlinearen Spektraltheorie. Im ersten Kapitel wird eine kurze Wiederholung der Definition und Eigenschaften des Spektrums und verschiedener Subspektren für gebundene lineare Operatoren vorgenommen. Im Anschluss werden einige numerische Eigenschaften für nichtlineare Operatoren eingeführt, die für die Beschreibung der Operatorenklassen nützlich sind, für die eine Spektraltheorie existiert. Da Spektralwerte eng mit den Lösbarkeitsresultaten für Operatorengleichungen zusammenhängen, werden verschiedene Bedingungen für die lokale oder globale Invertierbarkeit eines nichtlinearen Operators im dritten Kapitel aufgestellt. Die folgenden zwei Kapitel betreffen Spektren für bestimmte Klassen von stetigen, Lipschitz-stetigen und Differentialoperatoren. Diese Spektren passen jedoch einfach die entsprechenden Definitionen der linearen Theorie an, was ihre Anwendbarkeit in gewisser Weise einschränkt. Andere Spektren, die auf eine vollständig unterschiedliche Weise definiert werden, jedoch nützliche Anwendungsmöglichkeiten aufzuweisen scheinen, werden in den folgenden vier Kapiteln definiert und untersucht. Die restlichen drei Kapitel sind mehr auf die Anwendung ausgerichtet und behandeln nichtlineare Eigenwertprobleme, numerische Bereiche und ausgewählte Anwendungen für nichtlineare Probleme. Die einzigen Voraussetzungen für das Verständnis dieses Buchs sind gewisse Vorkenntnisse in Funktionsanalyse und Operatorentheorie. Es ist für Nicht-Fachleute gedacht, die einen Überblick über die Entwicklung der Spektraltheorie für nichtlineare Operatoren in den letzten 30 Jahren sowie einen kurzen Abriss über die verschiedenen Richtungen, in die sich die Forschung derzeit bewegt, erhalten möchten. In view of the eminent importance of spectral theory of linear operators in many fields of mathematics and physics, it is not surprising that various attempts have been made to define and study spectra also for nonlinear operators. This book provides a comprehensive and self-contained treatment of the theory, methods, and applications of nonlinear spectral theory. The first chapter briefly recalls the definition and properties of the spectrum and several subspectra for bounded linear operators. Then some numerical characteristics for nonlinear operators are introduced which are useful for describing those classes of operators for which there exists a spectral theory. Since spectral values are closely related to solvability results for operator equations, various conditions for the local or global invertibility of a nonlinear operator are collected in the third chapter. The following two chapters are concerned with spectra for certain classes of continuous, Lipschitz continuous, or differentiable operators. These spectra, however, simply adapt the corresponding definitions from the linear theory which somehow restricts their applicability. Other spectra which are defined in a completely different way, but seem to have useful applications, are defined and studied in the following four chapters. The remaining three chapters are more application-oriented and deal with nonlinear eigenvalue problems, numerical ranges, and selected applications to nonlinear problems. The only prerequisite for understanding this book is a modest background in functional analysis and operator theory. It is addressed to non-specialists who want to get an idea of the development of spectral theory for nonlinear operators in the last 30 years, as well as a glimpse of the diversity of the directions in which current research is moving. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Nonlinear theories. Spectral theory (Mathematics). Linearer Operator. Nichtlinearer Operator. Spektraltheorie. MATHEMATICS / General. bisacsh De Pascale, Espedito, author. aut http://id.loc.gov/vocabulary/relators/aut Vignoli, Alfonso, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications 9783110647099 Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 9783110637205 ZDB-23-GMA Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2008 9783110212129 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2008 9783110212136 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2008 9783110209082 ZDB-23-DMN print 9783110181432 https://doi.org/10.1515/9783110199260 https://www.degruyter.com/isbn/9783110199260 Cover https://www.degruyter.com/document/cover/isbn/9783110199260/original |
language |
English |
format |
eBook |
author |
Appell, Jürgen, Appell, Jürgen, De Pascale, Espedito, Vignoli, Alfonso, |
spellingShingle |
Appell, Jürgen, Appell, Jürgen, De Pascale, Espedito, Vignoli, Alfonso, Nonlinear Spectral Theory / De Gruyter Series in Nonlinear Analysis and Applications , Frontmatter -- Contents -- Introduction -- Chapter 1. Spectra of Bounded Linear -- Operators -- Chapter 2. Some Characteristics of Nonlinear -- Chapter 3. Invertibility of Nonlinear -- Chapter 4. The Rhodius and Neuberger -- Spectra -- Chapter 5. The Kachurovskij and Dörfner -- Chapter 6. The Furi–Martelli–Vignoli -- Spectrum -- Chapter 7. The Feng Spectrum -- Chapter 8. The Väth Phantom -- Chapter 9. Other Spectra -- Chapter 10. Nonlinear Eigenvalue Problems -- Chapter 11. Numerical Ranges of Nonlinear -- Chapter 12. Some Applications -- Backmatter |
author_facet |
Appell, Jürgen, Appell, Jürgen, De Pascale, Espedito, Vignoli, Alfonso, De Pascale, Espedito, De Pascale, Espedito, Vignoli, Alfonso, Vignoli, Alfonso, |
author_variant |
j a ja j a ja p e d pe ped a v av |
author_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author2 |
De Pascale, Espedito, De Pascale, Espedito, Vignoli, Alfonso, Vignoli, Alfonso, |
author2_variant |
p e d pe ped a v av |
author2_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author_sort |
Appell, Jürgen, |
title |
Nonlinear Spectral Theory / |
title_full |
Nonlinear Spectral Theory / Jürgen Appell, Espedito De Pascale, Alfonso Vignoli. |
title_fullStr |
Nonlinear Spectral Theory / Jürgen Appell, Espedito De Pascale, Alfonso Vignoli. |
title_full_unstemmed |
Nonlinear Spectral Theory / Jürgen Appell, Espedito De Pascale, Alfonso Vignoli. |
title_auth |
Nonlinear Spectral Theory / |
title_alt |
Frontmatter -- Contents -- Introduction -- Chapter 1. Spectra of Bounded Linear -- Operators -- Chapter 2. Some Characteristics of Nonlinear -- Chapter 3. Invertibility of Nonlinear -- Chapter 4. The Rhodius and Neuberger -- Spectra -- Chapter 5. The Kachurovskij and Dörfner -- Chapter 6. The Furi–Martelli–Vignoli -- Spectrum -- Chapter 7. The Feng Spectrum -- Chapter 8. The Väth Phantom -- Chapter 9. Other Spectra -- Chapter 10. Nonlinear Eigenvalue Problems -- Chapter 11. Numerical Ranges of Nonlinear -- Chapter 12. Some Applications -- Backmatter |
title_new |
Nonlinear Spectral Theory / |
title_sort |
nonlinear spectral theory / |
series |
De Gruyter Series in Nonlinear Analysis and Applications , |
series2 |
De Gruyter Series in Nonlinear Analysis and Applications , |
publisher |
De Gruyter, |
publishDate |
2008 |
physical |
1 online resource (408 p.) : Num. tab. Issued also in print. |
contents |
Frontmatter -- Contents -- Introduction -- Chapter 1. Spectra of Bounded Linear -- Operators -- Chapter 2. Some Characteristics of Nonlinear -- Chapter 3. Invertibility of Nonlinear -- Chapter 4. The Rhodius and Neuberger -- Spectra -- Chapter 5. The Kachurovskij and Dörfner -- Chapter 6. The Furi–Martelli–Vignoli -- Spectrum -- Chapter 7. The Feng Spectrum -- Chapter 8. The Väth Phantom -- Chapter 9. Other Spectra -- Chapter 10. Nonlinear Eigenvalue Problems -- Chapter 11. Numerical Ranges of Nonlinear -- Chapter 12. Some Applications -- Backmatter |
isbn |
9783110199260 9783110647099 9783110637205 9783110212129 9783110212136 9783110209082 9783110181432 |
issn |
0941-813X ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA320 |
callnumber-sort |
QA 3320 A67 42004EB |
url |
https://doi.org/10.1515/9783110199260 https://www.degruyter.com/isbn/9783110199260 https://www.degruyter.com/document/cover/isbn/9783110199260/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515/.7222 |
dewey-sort |
3515 47222 |
dewey-raw |
515/.7222 |
dewey-search |
515/.7222 |
doi_str_mv |
10.1515/9783110199260 |
oclc_num |
979635902 |
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Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2008 Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2008 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2008 |
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Nonlinear Spectral Theory / |
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Im ersten Kapitel wird eine kurze Wiederholung der Definition und Eigenschaften des Spektrums und verschiedener Subspektren für gebundene lineare Operatoren vorgenommen. Im Anschluss werden einige numerische Eigenschaften für nichtlineare Operatoren eingeführt, die für die Beschreibung der Operatorenklassen nützlich sind, für die eine Spektraltheorie existiert. Da Spektralwerte eng mit den Lösbarkeitsresultaten für Operatorengleichungen zusammenhängen, werden verschiedene Bedingungen für die lokale oder globale Invertierbarkeit eines nichtlinearen Operators im dritten Kapitel aufgestellt. Die folgenden zwei Kapitel betreffen Spektren für bestimmte Klassen von stetigen, Lipschitz-stetigen und Differentialoperatoren. Diese Spektren passen jedoch einfach die entsprechenden Definitionen der linearen Theorie an, was ihre Anwendbarkeit in gewisser Weise einschränkt. 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The only prerequisite for understanding this book is a modest background in functional analysis and operator theory. It is addressed to non-specialists who want to get an idea of the development of spectral theory for nonlinear operators in the last 30 years, as well as a glimpse of the diversity of the directions in which current research is moving.</subfield></datafield><datafield tag="530" ind1=" " ind2=" "><subfield code="a">Issued also in print.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. 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