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EBOOK
Author Grubb, Gerd.
Title Distributions and operators / Gerd Grubb.
Imprint New York : Springer, 2009.

LOCATION CALL # STATUS MESSAGE
 OHIOLINK SPRINGER EBOOKS    ONLINE  
View online
Author Grubb, Gerd.
Series Graduate texts in mathematics, 0072-5285 ; 252
Graduate texts in mathematics ; 252. 0072-5285
Subject Theory of distributions (Functional analysis)
Operator theory.
Hilbert space.
LOCATION CALL # STATUS MESSAGE
 OHIOLINK SPRINGER EBOOKS    ONLINE  
View online
Author Grubb, Gerd.
Series Graduate texts in mathematics, 0072-5285 ; 252
Graduate texts in mathematics ; 252. 0072-5285
Subject Theory of distributions (Functional analysis)
Operator theory.
Hilbert space.
Description 1 online resource (xii, 461 pages) : illustrations.
polychrome rdacc
Bibliography Note Includes bibliographical references (pages 451-456) and index.
Contents pt. I. Distributions and derivatives. Motivation and overview -- Function spaces and approximation -- Distributions. Examples and rules of calculus -- pt. II. Extensions and applications. Realizations and Sobolev spaces -- Fourier transformation of distributions -- Applications to differential operators. The Sobolev theorem -- pt. III. Pseudodifferential operators. Pseudodifferential operators on open sets -- Pseudodifferential operators on manifolds, index of elliptic operators -- pt. IV. Boundary value problems. Boundary value problems in a constant-coefficient case -- Pseudodifferential boundary operators -- Pseudodifferential methods for boundary value problems -- pt. V. Topics on Hilbert space operators. Unbounded linear operators -- Families of extensions -- Semigroups of operators -- A. Some notation and prerequisites -- B. Topological vector spaces -- Function spaces on sets with smooth boundary.
Summary 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 Calderon projector and its applications. Gerd Grubb is Professor of Mathematics at University of Copenhagen.
Note English.
Print version record.
ISBN 9780387848952
0387848959
0387848940
9780387848945
1441927433
9781441927439
9780387848945
ISBN/ISSN 10.1007/978-0-387-84895-2
Publisher # 12205455
OCLC # 310353034
Additional Format Print version: Grubb, Gerd. Distributions and operators. New York : Springer, 2009 9780387848945 0387848940 (DLC) 2008937582 (OCoLC)258078542


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