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Nonlinear Spectral Theory by Jürgen Appell, Espedito De Pascale, Alfonso Vignoli

Nonlinear Spectral Theory

by Jürgen Appell , Espedito De Pascale , Alfonso Vignoli
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Book cover type: Hardcover
  • ISBN13: 9783110181432
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: de Gruyter
  • Publisher Imprint: de Gruyter
  • Publication Date:
  • Pages: 419
  • Original Price: GBP 237.5
  • Language: English
  • Edition: N/A
  • Item Weight: 867 grams
  • BISAC Subject(s): Calculus

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 f�r 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 f�r gebundene lineare Operatoren vorgenommen. Im Anschluss werden einige numerische Eigenschaften f�r nichtlineare Operatoren eingef�hrt, die f�r die Beschreibung der Operatorenklassen n�tzlich sind, f�r die eine Spektraltheorie existiert. Da Spektralwerte eng mit den L�sbarkeitsresultaten f�r Operatorengleichungen zusammenh�ngen, werden verschiedene Bedingungen f�r die lokale oder globale Invertierbarkeit eines nichtlinearen Operators im dritten Kapitel aufgestellt. Die folgenden zwei Kapitel betreffen Spektren f�r 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 einschr�nkt. Andere Spektren, die auf eine vollst�ndig unterschiedliche Weise definiert werden, jedoch n�tzliche Anwendungsm�glichkeiten 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 ausgew�hlte Anwendungen f�r nichtlineare Probleme.

Die einzigen Voraussetzungen f�r das Verst�ndnis dieses Buchs sind gewisse Vorkenntnisse in Funktionsanalyse und Operatorentheorie. Es ist f�r Nicht-Fachleute gedacht, die einen �berblick �ber die Entwicklung der Spektraltheorie f�r nichtlineare Operatoren in den letzten 30 Jahren sowie einen kurzen Abriss �ber die verschiedenen Richtungen, in die sich die Forschung derzeit bewegt, erhalten m�chten.

Jürgen Appell is Professor at the Mathematics Institute of the University of Würzburg, Germany.

Espedito De Pascale is Professor at the Mathematics Department of the University of Calabria, Italy.

Alfonso Vignoli is Professor at the Mathematics Department of the University of Rome, Italy.

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