The Functional Calculus for Sectorial Operators
Language: English
Published by Birkhauser Verlag AG, CH, 2006
Series: Book 14 of 132 - Operator Theory: Advances and Applications
- Hardcover
- New
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This book contains a systematic and partly axiomatic treatment of the holomorphic functional calculus for unbounded sectorial operators. The account is generic so that it can be used to construct and interrelate holomorphic functional calculi for other types of unbounded operators. Particularly, an elegant unified approach to holomorphic semigroups is obtained. The last chapter describes applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis.
Seller Inventory # LU-9783764376970
- Title
- The Functional Calculus for Sectorial Operators
- Author
- Markus Haase
- Publisher
- Birkhauser Verlag AG, CH
- Publication year
- 2006
- Condition
- New
- Binding
- Hardback
- Language
- English
- ISBN 10
- 376437697X
- ISBN 13
- 9783764376970
- Edition
- 2006 ed.
- Series
- Book 14 of 132: Operator Theory: Advances and Applications
This book contains a systematic and partly axiomatic treatment of the holomorphic functional calculus for unbounded sectorial operators. The account is generic so that it can be used to construct and interrelate holomorphic functional calculi for other types of unbounded operators. Particularly, an elegant unified approach to holomorphic semigroups is obtained. The last chapter describes applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis.
"Synopsis" may belong to another edition of this title.
From the Back Cover
The present monograph deals with the functional calculus for unbounded operators in general and for sectorial operators in particular. Sectorial operators abound in the theory of evolution equations, especially those of parabolic type. They satisfy a certain resolvent condition that leads to a holomorphic functional calculus based on Cauchy-type integrals. Via an abstract extension procedure, this elementary functional calculus is then extended to a large class of (even meromorphic) functions.
With this functional calculus at hand, the book elegantly covers holomorphic semigroups, fractional powers, and logarithms. Special attention is given to perturbation results and the connection with the theory of interpolation spaces. A chapter is devoted to the exciting interplay between numerical range conditions, similarity problems and functional calculus on Hilbert spaces. Two chapters describe applications, for example to elliptic operators, to numerical approximations of parabolic equations, and to the maximal regularity problem.
This book is the first systematic account of a subject matter which lies in the intersection of operator theory, evolution equations, and harmonic analysis. It is an original and comprehensive exposition of the theory as a whole. Written in a clear style and optimally organised, it will prove useful for the advanced graduate as well as for the experienced researcher.
"About the title" may belong to another edition of this title.
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