Distributions and Operators by Gerd GrubbDistributions and Operators by Gerd Grubb

Distributions and Operators

byGerd Grubb

Paperback | November 23, 2010

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This book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. 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 ordinary and partial differential equations. In some of the latter chapters, the author illustrates how distribution theory is used to define pseudodifferential operators and how they are applied in the discussion of solvability of PDE, with or without boundary conditions. Each chapter has been enhanced with many exercises and examples, and a bibliography of relevant books and papers is collected at the end.A few of the unique topics include: (1) Boundary value problems in a constant-coefficient case; (2) Pseudodifferential Boundary Operators; (3) Families of extensions.Gerd Grubb is Professor of Mathematics at University of Copenhagen.
Title:Distributions and OperatorsFormat:PaperbackDimensions:464 pages, 23.5 × 15.5 × 0.07 inPublished:November 23, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:1441927433

ISBN - 13:9781441927439


Table of Contents

Preface.- Motivation and overview.- Function spaces and approximation.- Distributions: Examples and rules of calculus.- Realizations and Sobolev spaces.- Fourier transformation of distributions.- Applications to differential operators: The Sobolev theorem.- Pseudodifferential operators on open sets.- Pseudodifferential operators on manifolds, index of elliptic operators.- Boundary value problems in a constant-coefficient case.- Pseudodifferential boundary operators.- Pseudodifferential methods for boundary value problems.- Unbounded linear operators.- Families of extensions.- Semigroups of operators.- Some notation and prerequisites.- Topological vector spaces.- Function spaces on sets with smooth boundary.- Bibliography.- Index.

Editorial Reviews

From the reviews:"The book is directed at graduate students and 'researchers interested in its special topics' . . Distribution and Operators is split into five parts . . Well-written and scholarly, and equipped with many exercises of considerable pedagogical importance . Grubb's book is a fine contribution to the literature and should soon occupy a solid place among graduate texts for aspiring hard analysts specializing, e.g., in PDE." (Michael Berg, MAA Online, December, 2008)"This textbook gives a very clear introduction to distribution theory with emphasis on applications using functional analysis. In more advanced parts of the book, pseudodifferential methods are introduced, specially tailored for the study of boundary value problems. . The whole book is carefully and nicely written and each chapter ends with a number of exercises . . perfect for a Ph.D. course . . most of the material has been used frequently at the University of Copenhagen for several graduate courses." (Fabio Nicola, Mathematical Reviews, Issue 2010 b)"The book under review is a complete self-contained introduction to classical distribution theory with applications to the study of linear partial differential operators and, in particular, of (elliptic) boundary value problems, an area where the author has much experience . . very clear and precise. Almost all the results given in the book are proved, and the proofs give plenty of details and are easy to follow. There are a lot of examples and exercises . ." (David Jornet, Zentralblatt MATH, Vol. 1171, 2009)