The Resource Distributions and operators, Gerd Grubb
Distributions and operators, Gerd Grubb
Resource Information
The item Distributions and operators, Gerd Grubb represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Distributions and operators, Gerd Grubb represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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 constantcoefficient case; @* the pseudodifferential boundary operator calculus; @* the Calderón projector and its applications. Gerd Grubb is Professor of Mathematics at University of Copenhagen
 Language
 eng
 Extent
 1 online resource (xii, 461 pages)
 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 constantcoefficient 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
 Isbn
 9780387848952
 Label
 Distributions and operators
 Title
 Distributions and operators
 Statement of responsibility
 Gerd Grubb
 Subject

 Espace de Hilbert
 Hilbert space
 Hilbert space
 Hilbert space
 Hilbert space
 Operator theory
 Operator theory
 Operator theory
 Operator theory
 Theory of distributions (Functional analysis)
 Theory of distributions (Functional analysis)
 Theory of distributions (Functional analysis)
 Theory of distributions (Functional analysis)
 Théorie des distributions (Analyse fonctionnelle)
 Théorie des opérateurs
 Distributionstheorie
 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 constantcoefficient case; @* the pseudodifferential boundary operator calculus; @* the Calderón projector and its applications. Gerd Grubb is Professor of Mathematics at University of Copenhagen
 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
 Bibliography note
 Includes bibliographical references (pages 451456) 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 constantcoefficient 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
 10.1007/9780387848952
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 9780387848945
 Publisher number
 12205455
 Specific material designation
 remote
 System control number
 (OCoLC)310353034
 Label
 Distributions and operators, Gerd Grubb
 Bibliography note
 Includes bibliographical references (pages 451456) 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 constantcoefficient 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
 10.1007/9780387848952
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 9780387848945
 Publisher number
 12205455
 Specific material designation
 remote
 System control number
 (OCoLC)310353034
Subject
 Espace de Hilbert
 Hilbert space
 Hilbert space
 Hilbert space
 Hilbert space
 Operator theory
 Operator theory
 Operator theory
 Operator theory
 Theory of distributions (Functional analysis)
 Theory of distributions (Functional analysis)
 Theory of distributions (Functional analysis)
 Theory of distributions (Functional analysis)
 Théorie des distributions (Analyse fonctionnelle)
 Théorie des opérateurs
 Distributionstheorie
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