Cantitate/Preț
Produs
Total produse
Vezi coșul
Distribution Theory de Gerrit Dijk

Distribution Theory: De Gruyter Textbook

Autor Gerrit Dijk
en Limba Engleză Hardback – 15 mar 2013
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.
Citește tot Restrânge

Din seria De Gruyter Textbook

  • Chemistry of Nucleic Acids
    Preț: 40747 lei
  • 20% System Engineering with SysML
    Preț: 25603 lei
  • 19% Common Sense Relativity and Spacetime
    Preț: 51611 lei
  • 19% Partial Differential Equations Theory
    Preț: 45238 lei
  • 20% High Performance Parallel Runtimes
    Preț: 54469 lei
  • Mathematical Statistics
    Preț: 54108 lei
  • Multivariable Calculus and Differential Geometry
    Preț: 27370 lei
  • 8% Biorefineries
    Preț: 47195 lei
  • Learning and Teaching Mathematics using Simulations
    Preț: 33375 lei
  • 8% The Science of Innovation
    Preț: 38571 lei
  • 20% A Course in Mathematical Cryptography
    Preț: 32105 lei
  • Pseudodifferential and Singular Integral Operators
    Preț: 18922 lei
  • Stochastics
    Preț: 32591 lei
  • 8% Adaptive Numerical Solution of PDEs
    Preț: 41743 lei
  • 8% Rings and Their Modules
    Preț: 39807 lei
  • 8% Biotechnology
    Preț: 44697 lei
  • 5% Medical Physics
    Preț: 34735 lei
  • 8% Physics of Energy Conversion
    Preț: 50613 lei
  • A Primer in Combinatorics
    Preț: 33975 lei
  • Initiation à l'économie et à la gestion d'entreprise
    Preț: 31046 lei
  • Nonlinear Programming
    Preț: 37574 lei
  • 8% Industrial Inorganic Chemistry
    Preț: 46098 lei
  • Infinite Series in a History of Analysis
    Preț: 22243 lei
  • Narratology
    Preț: 15490 lei
  • 19% Insect Morphology and Phylogeny
    Preț: 56113 lei
  • 8% Compact NMR
    Preț: 46662 lei
  • Numerical Methods for Eigenvalue Problems
    Preț: 22711 lei
  • Asymptotic Statistics
    Preț: 26758 lei
  • 8% Sustainable Process Engineering
    Preț: 41219 lei
  • 8% Algebra in the Stone-Cech Compactification
    Preț: 49361 lei
  • 8% Nanoparticles
    Preț: 46662 lei
  • 8% Engineering Risk Management
    Preț: 46950 lei
  • 20% Industrial Software Applications
    Preț: 34058 lei
  • 8% Photogrammetry
    Preț: 47370 lei
  • 8% Semiconductor Spintronics
    Preț: 51679 lei
  • 9% Mathematical Statistics
    Preț: 72087 lei
  • 8% Integrated Bioprocess Engineering
    Preț: 48455 lei
  • Stochastic Finance
    Preț: 38586 lei
  • 8% Catalytic Reactors
    Preț: 40827 lei
  • 19% Basic Process Engineering Control
    Preț: 48807 lei
  • Political Parties in the Digital Age
    Preț: 25458 lei
  • 9% Lectures on the Topology of 3-Manifolds
    Preț: 71222 lei
  • 19% Electrospinning
    Preț: 45054 lei
  • 8% Wind Energy Harvesting
    Preț: 47173 lei
  • Elements of Partial Differential Equations
    Preț: 26807 lei
  • 23% Chemistry of the Non-Metals
    Preț: 72209 lei
  • 8% Dealing with Electronics
    Preț: 48264 lei
  • 20% Computational Technologies
    Preț: 25105 lei
  • 5% Liver Regeneration
    Preț: 45814 lei

Preț: 18608 lei

Puncte Express: 279

Carte tipărită la comandă

Livrare economică 21-27 mai

 Adaugă în coș

Wish list
Gift list
Am citit!
Adaugă în listă

Specificații

ISBN-13: 9783110295917
ISBN-10: 3110295911
Pagini: 120
Ilustrații: 1 schw.-w. Abb.
Dimensiuni: 175 x 246 x 14 mm
Greutate: 0.42 kg
Ediția:1. Auflage
Editura: De Gruyter
Colecția de Gruyter Textbook
Seria De Gruyter Textbook

Locul publicării:Berlin/Boston

Notă biografică

AD>Gerrit van Dijk, Leiden University, The Netherlands.

Cuprins

AD>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