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Cover: 9780387313412 | A Short Course on Operator Semigroups | Rainer Nagel (u. a.) | Buch
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A Short Course on Operator Semigroups
Buch von Rainer Nagel (u. a.)
Sprache: Englisch

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Beschreibung
ThetheoryofstronglycontinuoussemigroupsoflinearoperatorsonBanach spaces, operator semigroups for short, has become an indispensable tool in a great number of areas of modern mathematical analysis. In our Springer Graduate Text [EN00] we presented this beautiful theory, together with many applications, and tried to show the progress made since the pub- cation in 1957 of the now classical monograph [HP57] by E. Hille and R. Phillips. However, the wealth of results exhibited in our Graduate Text seems to have discouraged some of the potentially interested readers. With the present text we o?er a streamlined version that strictly sticks to the essentials. We have skipped certain parts, avoided the use of sophisticated arguments,and,occasionally,weakenedtheformulationofresultsandm- i?ed the proofs. However, to a large extent this book consists of excerpts taken from our Graduate Text, with some new material on positive se- groups added in Chapter VI. We hope that the present text will help students take their ?rst step into this interesting and lively research ?eld. On the other side, it should provide useful tools for the working mathematician. Acknowledgments This book is dedicated to our students. Without them we would not be able to do and to enjoy mathematics. Many of them read previous versions when it served as the text of our Seventh Internet Seminar 2003/04. Here Genni Fragnelli, Marc Preunkert and Mark C. Veraar were among the most active readers. Particular thanks go to Tanja Eisner, Vera Keicher, Agnes Radl for proposing considerable improvements in the ?nal version.
ThetheoryofstronglycontinuoussemigroupsoflinearoperatorsonBanach spaces, operator semigroups for short, has become an indispensable tool in a great number of areas of modern mathematical analysis. In our Springer Graduate Text [EN00] we presented this beautiful theory, together with many applications, and tried to show the progress made since the pub- cation in 1957 of the now classical monograph [HP57] by E. Hille and R. Phillips. However, the wealth of results exhibited in our Graduate Text seems to have discouraged some of the potentially interested readers. With the present text we o?er a streamlined version that strictly sticks to the essentials. We have skipped certain parts, avoided the use of sophisticated arguments,and,occasionally,weakenedtheformulationofresultsandm- i?ed the proofs. However, to a large extent this book consists of excerpts taken from our Graduate Text, with some new material on positive se- groups added in Chapter VI. We hope that the present text will help students take their ?rst step into this interesting and lively research ?eld. On the other side, it should provide useful tools for the working mathematician. Acknowledgments This book is dedicated to our students. Without them we would not be able to do and to enjoy mathematics. Many of them read previous versions when it served as the text of our Seventh Internet Seminar 2003/04. Here Genni Fragnelli, Marc Preunkert and Mark C. Veraar were among the most active readers. Particular thanks go to Tanja Eisner, Vera Keicher, Agnes Radl for proposing considerable improvements in the ?nal version.
Zusammenfassung

The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. It contains the fundamental results of the theory such as the Hille-Yoshida generation theorem, the bounded perturbation theorem, and the Trotter-Kato approximation theorem. It also treats the spectral theory of semigroups and its consequences for the qualitative behavior. The book is intended for students and researchers who want to become acquainted with the concept of semigroups in order to work with it in fields like partial and functional differential equations, stochastic processes, infinite dimensional control theory, or dynamical systems coming from physics or biology. Exercises are provided at the end of the chapters.

Inhaltsverzeichnis
Semigroups, Generators, and Resolvents.- Perturbation of Semigroups.- Approximation of Semigroups.- Spectral Theory and Asymptotics for Semigroups.- Positive Semigroups.
Details
Erscheinungsjahr: 2006
Fachbereich: Analysis
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Universitext
Inhalt: x
248 S.
ISBN-13: 9780387313412
ISBN-10: 0387313419
Sprache: Englisch
Herstellernummer: 11343400
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Nagel, Rainer
Engel, Klaus-Jochen
Hersteller: Springer US
Springer New York
Springer US, New York, N.Y.
Universitext
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 19 mm
Von/Mit: Rainer Nagel (u. a.)
Erscheinungsdatum: 06.06.2006
Gewicht: 0,559 kg
Artikel-ID: 102248189
Zusammenfassung

The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. It contains the fundamental results of the theory such as the Hille-Yoshida generation theorem, the bounded perturbation theorem, and the Trotter-Kato approximation theorem. It also treats the spectral theory of semigroups and its consequences for the qualitative behavior. The book is intended for students and researchers who want to become acquainted with the concept of semigroups in order to work with it in fields like partial and functional differential equations, stochastic processes, infinite dimensional control theory, or dynamical systems coming from physics or biology. Exercises are provided at the end of the chapters.

Inhaltsverzeichnis
Semigroups, Generators, and Resolvents.- Perturbation of Semigroups.- Approximation of Semigroups.- Spectral Theory and Asymptotics for Semigroups.- Positive Semigroups.
Details
Erscheinungsjahr: 2006
Fachbereich: Analysis
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Universitext
Inhalt: x
248 S.
ISBN-13: 9780387313412
ISBN-10: 0387313419
Sprache: Englisch
Herstellernummer: 11343400
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Nagel, Rainer
Engel, Klaus-Jochen
Hersteller: Springer US
Springer New York
Springer US, New York, N.Y.
Universitext
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 19 mm
Von/Mit: Rainer Nagel (u. a.)
Erscheinungsdatum: 06.06.2006
Gewicht: 0,559 kg
Artikel-ID: 102248189
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