Coverart for item
The Resource Distributions and operators, Gerd Grubb

Distributions and operators, Gerd Grubb

Label
Distributions and operators
Title
Distributions and operators
Statement of responsibility
Gerd Grubb
Creator
Subject
Language
eng
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 Calderón projector and its applications. Gerd Grubb is Professor of Mathematics at University of Copenhagen
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Grubb, Gerd
Dewey number
515.782
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA324
LC item number
.G778 2009eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Graduate texts in mathematics,
Series volume
252
http://library.link/vocab/subjectName
  • Theory of distributions (Functional analysis)
  • Operator theory
  • Hilbert space
  • Théorie des distributions (Analyse fonctionnelle)
  • Théorie des opérateurs
  • Espace de Hilbert
  • Hilbert space
  • Theory of distributions (Functional analysis)
  • Operator theory
  • Hilbert space
  • Operator theory
  • Theory of distributions (Functional analysis)
  • Distributionstheorie
Label
Distributions and operators, Gerd Grubb
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 451-456) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
310353034
Dimensions
unknown
Extent
1 online resource (xii, 461 pages)
Form of item
online
Isbn
9780387848952
Lccn
2008937582
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-387-84895-2
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-0-387-84894-5
Publisher number
12205455
Specific material designation
remote
System control number
(OCoLC)310353034
Label
Distributions and operators, Gerd Grubb
Publication
Bibliography note
Includes bibliographical references (pages 451-456) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
310353034
Dimensions
unknown
Extent
1 online resource (xii, 461 pages)
Form of item
online
Isbn
9780387848952
Lccn
2008937582
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-387-84895-2
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-0-387-84894-5
Publisher number
12205455
Specific material designation
remote
System control number
(OCoLC)310353034

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