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 constant-coefficient 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 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
- Isbn
- 9780387848945
- 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 constant-coefficient 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 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
- 9780387848945
- 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
- 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
- 9780387848945
- 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
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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Distributions-and-operators-Gerd-Grubb/i7cvwaDre1A/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Distributions-and-operators-Gerd-Grubb/i7cvwaDre1A/">Distributions and operators, Gerd Grubb</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
