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＜電子ブック＞
Distributions and Operators / by Gerd Grubb
(Graduate Texts in Mathematics. ISSN:21975612 ; 252)

版	1st ed. 2009.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	XII, 464 p : online resource
著者標目	*Grubb, Gerd author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Differential equations FREE:Functional Analysis FREE:Differential Equations
一般注記	Distributions and derivatives -- Motivation and overview -- Function spaces and approximation -- Distributions. Examples and rules of calculus -- Extensions and applications -- Realizations and Sobolev spaces -- Fourier transformation of distributions -- Applications to differential operators. The Sobolev theorem -- Pseudodifferential operators -- Pseudodifferential operators on open sets -- Pseudodifferential operators on manifolds, index of elliptic operators -- Boundary value problems -- Boundary value problems in a constant-coefficient case -- Pseudodifferential boundary operators -- Pseudodifferential methods for boundary value problems -- Topics on Hilbert space operators -- Unbounded linear operators -- Families of extensions -- Semigroups of operators This book gives an introduction to distribution theory, in the spirit of Laurent Schwartz. Additionally, the aim is to show how the theory is combined with the study of operators in Hilbert space by methods of functional analysis, with applications to partial and ordinary differential equations. Here, the author provides an introduction to unbounded operators in Hilbert space, including a complete theory of extensions of operators, and applications using contraction semigroups. In more advanced parts of the book, the author shows how distribution theory is used to define pseudodifferential operators on manifolds, and gives a detailed introduction to the pseudodifferential boundary operator calculus initiated by Boutet de Monvel, which allows a modern treatment of elliptic boundary value problems. This book is aimed at graduate students, as well as researchers interested in its special topics, and as such, the author provides careful explanations along with complete proofs, and a bibliography of relevant books and papers. Each chapter has been enhanced with many exercises and examples. Unique topics include: * the interplay between distribution theory and concrete operators; * families of extensions of nonselfadjoint operators; * an illustration of the solution maps between distribution spaces by a fully worked out constant-coefficient case; * the pseudodifferential boundary operator calculus; * the Calderón projector and its applications. Gerd Grubb is Professor of Mathematics at University of Copenhagen HTTP:URL=https://doi.org/10.1007/978-0-387-84895-2

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