The Functional Calculus for Sectorial Operators

  • Markus Haase

Part of the Operator Theory: Advances and Applications book series (OT, volume 169)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Markus Haase
    Pages 1-17
  3. Markus Haase
    Pages 61-89
  4. Markus Haase
    Pages 91-104
  5. Markus Haase
    Pages 105-129
  6. Markus Haase
    Pages 131-169
  7. Markus Haase
    Pages 171-218
  8. Markus Haase
    Pages 219-250
  9. Markus Haase
    Pages 251-278
  10. Back Matter
    Pages 279-392

About this book

Introduction

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.

Keywords

Hilbert space Operator theory function space functional analysis functional calculus interpolation semigroup

Authors and affiliations

  • Markus Haase
    • 1
  1. 1.Department of Pure MathematicsUniversity of LeedsLeedsUK

Bibliographic information

  • DOI https://doi.org/10.1007/3-7643-7698-8
  • Copyright Information Birkhäuser Basel 2006
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-7697-0
  • Online ISBN 978-3-7643-7698-7
  • About this book