Overview
- First systematic account of functional calculus for sectorial (and other types of unbounded) operators
- Emphasizes the calculus aspect of the matter, thus paving the way for making functional calculus a working tool
- A chapter on fractional powers combines elegance with comprehensibility, even in the most general setting
- The Hilbert space results, duly arranged and comprehensibly presented, appear in book form for the first time
- Includes supplementary material: sn.pub/extras
Part of the book series: Operator Theory: Advances and Applications (OT, volume 169)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (9 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: The Functional Calculus for Sectorial Operators
Authors: Markus Haase
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/3-7643-7698-8
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2006
Hardcover ISBN: 978-3-7643-7697-0Published: 14 June 2006
eBook ISBN: 978-3-7643-7698-7Published: 18 August 2006
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: XIV, 394
Topics: Operator Theory, Functional Analysis