---

＜電子ブック＞
Functional Calculus of Pseudodifferential Boundary Problems / by Gerd Grubb
(Progress in Mathematics. ISSN:2296505X ; 65)

版	2nd ed. 1996.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	1996
本文言語	英語
大きさ	IX, 526 p : online resource
著者標目	*Grubb, Gerd author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Functional analysis LCSH:Differential equations FREE:Analysis FREE:Functional Analysis FREE:Differential Equations
一般注記	1. Standard pseudodifferential boundary problems and their realizations -- 2. The calculus of parameter-dependent operators -- 3. Parametrix and resolvent constructions -- 4. Some applications -- Appendix. Various prerequisites 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 Many proofs have been replaced by new and simpler arguments, giving better results and clearer insights.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 HTTP:URL=https://doi.org/10.1007/978-1-4612-0769-6

 類似資料