Coverart for item
The Resource Distribution Theory : Convolution, Fourier Transform, and Laplace Transform

Distribution Theory : Convolution, Fourier Transform, and Laplace Transform

Label
Distribution Theory : Convolution, Fourier Transform, and Laplace Transform
Title
Distribution Theory
Title remainder
Convolution, Fourier Transform, and Laplace Transform
Creator
Subject
Language
eng
Summary
The theory of distributions has numerous applications and is extensively used in mathematics, physics and engineering. There is however relatively little elementary expository literature on distribution theory. This book is intended as an introduction. Starting with the elementary theory of distributions, it proceeds to convolution products of distributions, Fourier and Laplace transforms, tempered distributions, summable distributions and applications. The theory is illustrated by several examples, mostly beginning with the case of the real line and then followed by examples in higher dimensi
Member of
Cataloging source
EBLCP
http://library.link/vocab/creatorName
Dijk, Gerrit
Dewey number
515.782
Index
index present
LC call number
QA324
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
De Gruyter Textbook
http://library.link/vocab/subjectName
  • Theory of distributions (Functional analysis)
  • MATHEMATICS
  • Theory of distributions (Functional analysis)
Label
Distribution Theory : Convolution, Fourier Transform, and Laplace Transform
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; 1 Introduction; 2 Definition and First Properties of Distributions; 2.1 Test Functions; 2.2 Distributions; 2.3 Support of a Distribution; 3 Differentiating Distributions; 3.1 Definition and Properties; 3.2 Examples; 3.3 The Distributions x+?-1(??0,-1,-2 ...)*; 3.4 Exercises; 3.5 Green's Formula and Harmonic Functions; 3.6 Exercises; 4 Multiplication and Convergence of Distributions; 4.1 Multiplication with a C8 Function; 4.2 Exercises; 4.3 Convergence in D'; 4.4 Exercises; 5 Distributions with Compact Support; 5.1 Definition and Properties; 5.2 Distributions Supported at the Origin
  • 5.3 Taylor's Formula for Rn5.4 Structure of a Distribution*; 6 Convolution of Distributions; 6.1 Tensor Product of Distributions; 6.2 Convolution Product of Distributions; 6.3 Associativity of the Convolution Product; 6.4 Exercises; 6.5 Newton Potentials and Harmonic Functions; 6.6 Convolution Equations; 6.7 Symbolic Calculus of Heaviside; 6.8 Volterra Integral Equations of the Second Kind; 6.9 Exercises; 6.10 Systems of Convolution Equations*; 6.11 Exercises; 7 The Fourier Transform; 7.1 Fourier Transform of a Function on R; 7.2 The Inversion Theorem; 7.3 Plancherel's Theorem
  • 7.4 Differentiability Properties7.5 The Schwartz Space S(R); 7.6 The Space of Tempered Distributions S'(R); 7.7 Structure of a Tempered Distribution*; 7.8 Fourier Transform of a Tempered Distribution; 7.9 Paley Wiener Theorems on R*; 7.10 Exercises; 7.11 Fourier Transform in Rn; 7.12 The Heat or Diffusion Equation in One Dimension; 8 The Laplace Transform; 8.1 Laplace Transform of a Function; 8.2 Laplace Transform of a Distribution; 8.3 Laplace Transform and Convolution; 8.4 Inversion Formula for the Laplace Transform; 9 Summable Distributions*; 9.1 Definition and Main Properties
  • 9.2 The Iterated Poisson Equation9.3 Proof of the Main Theorem; 9.4 Canonical Extension of a Summable Distribution; 9.5 Rank of a Distribution; 10 Appendix; 10.1 The Banach Steinhaus Theorem; 10.2 The Beta and Gamma Function; 11 Hints to the Exercises; References; Index
Control code
851970512
Dimensions
unknown
Extent
1 online resource (120 pages)
Form of item
online
Isbn
9783110298512
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote
System control number
(OCoLC)851970512
Label
Distribution Theory : Convolution, Fourier Transform, and Laplace Transform
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; 1 Introduction; 2 Definition and First Properties of Distributions; 2.1 Test Functions; 2.2 Distributions; 2.3 Support of a Distribution; 3 Differentiating Distributions; 3.1 Definition and Properties; 3.2 Examples; 3.3 The Distributions x+?-1(??0,-1,-2 ...)*; 3.4 Exercises; 3.5 Green's Formula and Harmonic Functions; 3.6 Exercises; 4 Multiplication and Convergence of Distributions; 4.1 Multiplication with a C8 Function; 4.2 Exercises; 4.3 Convergence in D'; 4.4 Exercises; 5 Distributions with Compact Support; 5.1 Definition and Properties; 5.2 Distributions Supported at the Origin
  • 5.3 Taylor's Formula for Rn5.4 Structure of a Distribution*; 6 Convolution of Distributions; 6.1 Tensor Product of Distributions; 6.2 Convolution Product of Distributions; 6.3 Associativity of the Convolution Product; 6.4 Exercises; 6.5 Newton Potentials and Harmonic Functions; 6.6 Convolution Equations; 6.7 Symbolic Calculus of Heaviside; 6.8 Volterra Integral Equations of the Second Kind; 6.9 Exercises; 6.10 Systems of Convolution Equations*; 6.11 Exercises; 7 The Fourier Transform; 7.1 Fourier Transform of a Function on R; 7.2 The Inversion Theorem; 7.3 Plancherel's Theorem
  • 7.4 Differentiability Properties7.5 The Schwartz Space S(R); 7.6 The Space of Tempered Distributions S'(R); 7.7 Structure of a Tempered Distribution*; 7.8 Fourier Transform of a Tempered Distribution; 7.9 Paley Wiener Theorems on R*; 7.10 Exercises; 7.11 Fourier Transform in Rn; 7.12 The Heat or Diffusion Equation in One Dimension; 8 The Laplace Transform; 8.1 Laplace Transform of a Function; 8.2 Laplace Transform of a Distribution; 8.3 Laplace Transform and Convolution; 8.4 Inversion Formula for the Laplace Transform; 9 Summable Distributions*; 9.1 Definition and Main Properties
  • 9.2 The Iterated Poisson Equation9.3 Proof of the Main Theorem; 9.4 Canonical Extension of a Summable Distribution; 9.5 Rank of a Distribution; 10 Appendix; 10.1 The Banach Steinhaus Theorem; 10.2 The Beta and Gamma Function; 11 Hints to the Exercises; References; Index
Control code
851970512
Dimensions
unknown
Extent
1 online resource (120 pages)
Form of item
online
Isbn
9783110298512
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote
System control number
(OCoLC)851970512

Library Locations

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      1 University Blvd, St. Louis, MO, 63121, US
      38.710138 -90.311107
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