Progress in Mathematics

Functional Calculus of Pseudodifferential Boundary Problems

Authors: Grubb, Gerd

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About this book

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 Many proofs have been replaced by new and simpler arguments, giving better results and clearer insights.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

Reviews

"The book under review certainly belongs to the standard references in the theory of pseudodifferential operators. It is thoroughly written and offers a valuable source of information..."

--ZAA

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

--Mathematical Reviews (From a review of the first edition)


Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-1-4612-0769-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-0-8176-3738-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.99
price for USA in USD
  • ISBN 978-1-4612-6895-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Functional Calculus of Pseudodifferential Boundary Problems
Authors
Series Title
Progress in Mathematics
Series Volume
65
Copyright
1996
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-1-4612-0769-6
DOI
10.1007/978-1-4612-0769-6
Hardcover ISBN
978-0-8176-3738-5
Softcover ISBN
978-1-4612-6895-6
Series ISSN
0743-1643
Edition Number
2
Number of Pages
IX, 526
Topics