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Distribution Theory: Convolution, Fourier Transform, And Laplace Transform (De Gruyter Textbook) - Van Dijk, Gerrit
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Van Dijk, Gerrit:

Distribution Theory: Convolution, Fourier Transform, And Laplace Transform (De Gruyter Textbook) - primeira edição

2013, ISBN: 9783110295917

Edição encadernada

De Gruyter, Gebundene Ausgabe, Auflage: 1, 120 Seiten, Publiziert: 2013-03-15T00:00:01Z, Produktgruppe: Buch, 0.22 kg, Verkaufsrang: 1890939, Ingenieurwissenschaft & Technik, Naturwissens… mais…

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Dijk, Gerrit:

Distribution Theory Convolution, Fourier Transform, and Laplace Transform - encadernado, livro de bolso

2013, ISBN: 3110295911

Gebundene Ausgabe Analysis, Calculus, Analysis / Fourieranalysis, Fourieranalysis, Fourier-Transformation, Infinitesimalrechnung, distributions; DistibutionTheory; GeneralizedFunctions; … mais…

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Distribution Theory Convolution, Fourier Transform, and Laplace Transform - Dijk, Gerrit
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Dijk, Gerrit:
Distribution Theory Convolution, Fourier Transform, and Laplace Transform - encadernado, livro de bolso

2013

ISBN: 3110295911

Gebundene Ausgabe Analysis, Calculus, Analysis / Fourieranalysis, Fourieranalysis, Fourier-Transformation, Infinitesimalrechnung, distributions; DistibutionTheory; GeneralizedFunctions; … mais…

Custos de envio:Versandkosten innerhalb der BRD. (EUR 2.95) MARZIES.de Buch- und Medienhandel, 14621 Schönwalde-Glien
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Distribution Theory Convolution, Fourier Transform, and Laplace Transform - Dijk, Gerrit
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Dijk, Gerrit:
Distribution Theory Convolution, Fourier Transform, and Laplace Transform - encadernado, livro de bolso

2013, ISBN: 3110295911

Gebundene Ausgabe Analysis, Calculus, Analysis / Fourieranalysis, Fourieranalysis, Fourier-Transformation, Infinitesimalrechnung, distributions; DistibutionTheory; GeneralizedFunctions; … mais…

Custos de envio:Frais d'envoi en Allemagne. (EUR 2.95) MARZIES.de Buch- und Medienhandel, 14621 Schönwalde-Glien
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Distribution Theory Convolution, Fourier Transform, and Laplace Transform - Dijk, Gerrit
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Dijk, Gerrit:
Distribution Theory Convolution, Fourier Transform, and Laplace Transform - encadernado, livro de bolso

2013, ISBN: 3110295911

Gebundene Ausgabe Analysis, Calculus, Analysis / Fourieranalysis, Fourieranalysis, Fourier-Transformation, Infinitesimalrechnung, distributions; DistibutionTheory; GeneralizedFunctions; … mais…

Custos de envio:Frais d'envoi en Allemagne. (EUR 2.95) MARZIES.de Buch- und Medienhandel, 14621 Schönwalde-Glien

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Distribution Theory: Convolution, Fourier Transform, And Laplace Transform (De Gruyter Textbook)

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 dimensions. This is a justified and practical approach, it helps the reader to become familiar with the subject. A moderate number of exercises are added. It is suitable for a one-semester course at the advanced undergraduate or beginning graduatelevelor for self-study.

Dados detalhados do livro - Distribution Theory: Convolution, Fourier Transform, And Laplace Transform (De Gruyter Textbook)


EAN (ISBN-13): 9783110295917
ISBN (ISBN-10): 3110295911
Livro de capa dura
Livro de bolso
Ano de publicação: 2013
Editor/Editora: De Gruyter
109 Páginas
Peso: 0,223 kg
Língua: Englisch

Livro na base de dados desde 2007-07-05T00:32:54+01:00 (Lisbon)
Página de detalhes modificada pela última vez em 2024-04-09T09:41:04+01:00 (Lisbon)
Número ISBN/EAN: 9783110295917

Número ISBN - Ortografia alternativa:
3-11-029591-1, 978-3-11-029591-7
Ortografia alternativa e termos de pesquisa relacionados:
Autor do livro: van dijk
Título do livro: fourier, convolution, text and, laplace transform, gruyter textbook


Dados da editora

Autor: Gerrit Dijk
Título: De Gruyter Textbook; Distribution Theory - Convolution, Fourier Transform, and Laplace Transform
Editora: De Gruyter
109 Páginas
Ano de publicação: 2013-03-15
Berlin/Boston
Impresso / Feito em
Peso: 0,223 kg
Língua: Inglês
24,95 € (DE)
24,95 € (AT)
Available
1 b/w ill.

BB; Taschenbuch / Mathematik; Mathematische Analysis, allgemein; Verstehen; MAT003000 MATHEMATICS / Applied; MAT011000 MATHEMATICS / Game Theory; MAT025000 MATHEMATICS / Recreations & Games; MAT033000 MATHEMATICS / Vector Analysis; MAT037000 MATHEMATICS / Functional Analysis; Calculus & mathematical analysis; Applied mathematics; Maths for scientists; Mathematik; Distributions; Distibution Theory; Generalized Functions; Distribution Theory; Fourier Transform; Laplace Transform; Tempered Distribution; Heat Equation; Textbook; EA

Preface 2 1 Definition and first properties of distributions 7 1.1 Test functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Support of a distribution . . . . . . . . . . . . . . . . . . . . . 10 2 Differentiating distributions 13 2.1 Definition and properties . . . . . . . . . . . . . . . . . . . . . 13 2.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 The distributions x−1+ ( 6= 0,−1,−2, . . . )* . . . . . . . . . . 16 2.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5 Green’s formula and harmonic functions . . . . . . . . . . . . 19 2.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3 Multiplication and convergence of distributions 27 3.1 Multiplication with a C1 function . . . . . . . . . . . . . . . 27 3.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3 Convergence in D0 . . . . . . . . . . . . . . . . . . . . . . . . 28 3.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4 Distributions with compact support 31 4.1 Definition and properties . . . . . . . . . . . . . . . . . . . . . 31 4.2 Distributions supported at the origin . . . . . . . . . . . . . . 32 4.3 Taylor’s formula for Rn . . . . . . . . . . . . . . . . . . . . . 33 4.4 Structure of a distribution* . . . . . . . . . . . . . . . . . . . 34 5 Convolution of distributions 36 5.1 Tensor product of distributions . . . . . . . . . . . . . . . . . 36 5.2 Convolution product of distributions . . . . . . . . . . . . . . 38 5.3 Associativity of the convolution product . . . . . . . . . . . . 44 5.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.5 Newton potentials and harmonic functions . . . . . . . . . . . 45 5.6 Convolution equations . . . . . . . . . . . . . . . . . . . . . . 47 5.7 Symbolic calculus of Heaviside . . . . . . . . . . . . . . . . . 50 5.8 Volterra integral equations of the second kind . . . . . . . . . 52 5.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.10 Systems of convolution equations* . . . . . . . . . . . . . . . 55 5.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 6 The Fourier transform 57 6.1 Fourier transform of a function on R . . . . . . . . . . . . . . 57 6.2 The inversion theorem . . . . . . . . . . . . . . . . . . . . . . 60 6.3 Plancherel’s theorem . . . . . . . . . . . . . . . . . . . . . . . 61 6.4 Differentiability properties . . . . . . . . . . . . . . . . . . . . 62 6.5 The Schwartz space S(R) . . . . . . . . . . . . . . . . . . . . 63 6.6 The space of tempered distributions S0(R) . . . . . . . . . . . 65 6.7 Structure of a tempered distribution* . . . . . . . . . . . . . 66 6.8 Fourier transform of a tempered distribution . . . . . . . . . 67 6.9 Paley Wiener theorems on R* . . . . . . . . . . . . . . . . . . 69 6.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 6.11 Fourier transform in Rn . . . . . . . . . . . . . . . . . . . . . 73 6.12 The heat or diffusion equation in one dimension . . . . . . . . 75 7 The Laplace transform 79 7.1 Laplace transform of a function . . . . . . . . . . . . . . . . . 79 7.2 Laplace transform of a distribution . . . . . . . . . . . . . . . 80 7.3 Laplace transform and convolution . . . . . . . . . . . . . . . 81 7.4 Inversion formula for the Laplace transform . . . . . . . . . . 84 8 Summable distributions* 87 8.1 Definition and main properties . . . . . . . . . . . . . . . . . 87 8.2 The iterated Poisson equation . . . . . . . . . . . . . . . . . . 88 8.3 Proof of the main theorem . . . . . . . . . . . . . . . . . . . . 89 8.4 Canonical extension of a summable distribution . . . . . . . . 91 8.5 Rank of a distribution . . . . . . . . . . . . . . . . . . . . . . 93 9 Appendix 96 9.1 The Banach-Steinhaus theorem . . . . . . . . . . . . . . . . . 96 9.2 The beta and gamma function . . . . . . . . . . . . . . . . . 103 Bibliography 108 Index 109

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