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Table of contents (5 chapters)
Keywords
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 Many proofs have been replaced by new and simpler arguments, giving better results and clearer insights.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.
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)
Authors and Affiliations
Bibliographic Information
Book Title: Functional Calculus of Pseudodifferential Boundary Problems
Authors: Gerd Grubb
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-1-4612-0769-6
Publisher: Birkhäuser Boston, MA
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eBook Packages: Springer Book Archive
Copyright Information: Birkhäuser Boston 1996
Hardcover ISBN: 978-0-8176-3738-5Published: 26 January 1996
Softcover ISBN: 978-1-4612-6895-6Published: 06 February 2013
eBook ISBN: 978-1-4612-0769-6Published: 06 December 2012
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 2
Number of Pages: IX, 526
Topics: Analysis, Functional Analysis, Partial Differential Equations, Ordinary Differential Equations