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Functional Calculus of Pseudodifferential Boundary Problems

  • Gerd Grubb

Part of the Progress in Mathematics book series (PM, volume 65)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Gerd Grubb
    Pages 1-14
  3. Gerd Grubb
    Pages 292-367
  4. Gerd Grubb
    Pages 368-477
  5. Back Matter
    Pages 478-526

About this book

Introduction

Pseudodifferential methods are central to the study of partial differential equations, because they permit an "algebraization." A replacement of compositions of operators in n-space by simpler product rules for thier symbols. The main purpose of this book is to set up an operational calculus for operators defined from differential and pseudodifferential boundary values problems via a resolvent construction. A secondary purposed is to give a complete treatment of the properties of the calculus of pseudodifferential boundary problems with transmission, both the first version by Boutet de Monvel (brought completely up to date in this edition) and in version containing a parameter running in an unbounded set. And finally, the book presents some applications to evolution problems, index theory, fractional powers, spectral theory and singular perturbation theory.

In this second edition the author has extended the scope and applicability of the calculus wit original contributions and perspectives developed in the years since the first edition. A main improvement is the inclusion of globally estimated symbols, allowing a treatment of operators on noncompact manifolds. Many proofs have been replaced by new and simpler arguments, giving better results and clearer insights. The applications to specific problems have been adapted to use these improved and more concrete techniques. Interest continues to increase among geometers and operator theory specialists in the Boutet de Movel calculus and its various generalizations. Thus the book’s improved proofs and modern points of view will be useful to research mathematicians and to graduate students studying partial differential equations and pseudodifferential operators.

From a review of the first edition:

"The book is well written, and it will certainly be useful for everyone interested in boundary value problems and spectral theory."

-Mathematical Reviews, July 1988

Keywords

Algebra Manifold calculus equation function partial differential equation proof

Authors and affiliations

  • Gerd Grubb
    • 1
  1. 1.Københavns Universitets Matematiske InstitutKøbenhavn ØDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0769-6
  • Copyright Information Birkhäuser Boston 1996
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6895-6
  • Online ISBN 978-1-4612-0769-6
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site