Gerd Grubb: Distributions and Operators

Cover: 9781441927439 | Distributions and Operators | Gerd Grubb | Taschenbuch | Paperback

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Beschreibung

This textbook gives an introduction to distribution theory with emphasis on applications using functional analysis. In more advanced parts of the book, pseudodi?erential methods are introduced. Distributiontheoryhasbeen developedprimarilytodealwithpartial(and ordinary) di?erential equations in general situations. Functional analysis in, say, Hilbert spaces has powerful tools to establish operators with good m- ping properties and invertibility properties. A combination of the two allows showing solvability of suitable concrete partial di?erential equations (PDE). When partial di?erential operators are realized as operators in L (?) for 2 n anopensubset?ofR ,theycomeoutasunboundedoperators.Basiccourses infunctionalanalysisareoftenlimitedtothestudyofboundedoperators,but we here meet the necessityof treating suitable types ofunbounded operators; primarily those that are densely de?ned and closed. Moreover, the emphasis in functional analysis is often placed on selfadjoint or normal operators, for which beautiful results can be obtained by means of spectral theory, but the cases of interest in PDE include many nonselfadjoint operators, where diagonalizationbyspectraltheoryisnotveryuseful.Weincludeinthisbooka chapter on unbounded operatorsin Hilbert space (Chapter 12),where classes of convenient operators are set up, in particular the variational operators, including selfadjoint semibounded cases (e.g., the Friedrichs extension of a symmetric operator), but with a much wider scope. Whereas the functional analysis de?nition of the operators is relatively clean and simple, the interpretation to PDE is more messy and complicated.

Zusammenfassung

Provides a more detailed and explicit elementary access to distribution theory than is found in most other books.

Contains unique topics

The author has made this easily accessible to advanced undergraduates, as well as graduates

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2010
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Graduate Texts in Mathematics
Inhalt:	xii 464 S. 8 s/w Illustr.
ISBN-13:	9781441927439
ISBN-10:	1441927433
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Grubb, Gerd
Auflage:	Softcover reprint of hardcover 1st ed. 2009
Hersteller:	Springer New York Springer US, New York, N.Y. Graduate Texts in Mathematics
Maße:	235 x 155 x 26 mm
Von/Mit:	Gerd Grubb
Erscheinungsdatum:	23.11.2010
Gewicht:	0,715 kg