Functional Calculus of Pseudodifferential Boundary Problems: 65 (Progress in Mathematics, 65) - Hardcover

Grubb, Gerd

 
9780817637385: Functional Calculus of Pseudodifferential Boundary Problems: 65 (Progress in Mathematics, 65)
Hardcover
ISBN 10: 0817637389 ISBN 13: 9780817637385
Verlag: Birkhäuser, 1996

Inhaltsangabe

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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Von der hinteren Coverseite

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

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Verlag
Birkhäuser
Erscheinungsdatum
1996
Sprache
Englisch
ISBN 10 
0817637389
ISBN 13 
9780817637385
Einband
Tapa dura
Auflage
1
Anzahl der Seiten
540
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar