Functional Calculus of Pseudodifferential Boundary Problems / Edition 2

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Pseudodifferential methods are central to the study of partial differential equations, because they permit an "algebraization." 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. 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.
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Editorial Reviews

A presentation of operational calculus defined from differential and pseudodifferential boundary value problems via a resolvent construction. Full treatment is given to the properties of the calculus with transmission by Boutet de Monvel, and in versions containing a parameter running in an unbounded set. Other applications include evolution problems, index theory, fractional powers, spectral theory, and singular perturbation theory. The second edition extends the scope and applicability of the calculus and features simpler arguments achieving clearer insights in a more attractive format. Annotation c. Book News, Inc., Portland, OR (
From the Publisher

"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..."


"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)

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Product Details

  • ISBN-13: 9780817637385
  • Publisher: Birkhauser Verlag
  • Publication date: 1/1/1996
  • Series: Progress in Mathematics Series, #65
  • Edition description: 2nd ed. 1996
  • Edition number: 2
  • Pages: 526
  • Product dimensions: 1.19 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Introduction.-Standard Pseudodifferential Boundary Problems and their Realizations.-The Calculus of Parameter-Dependent Operators.-Parametrix and Resolvent Constructions.-Some Applications.-Appendix: Various Prerequisites.-Bibliography.-Index.
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