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221028 ||| eng |
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|a 9780123965608
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|a 9780080956763
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|a 0123965608
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4 |
|a QA324
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|a Kanwal, Ram P.
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| 245 |
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|a Generalized functions
|b theory and technique
|c Ram P. Kanwal
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| 260 |
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|a New York
|b Academic Press
|c 1983, 1983
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| 300 |
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|a xiii, 428 pages
|b illustrations
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|a Front Cover; Generalized Functions: Theory and Technique; Copyright Page; Contents; PREFACE; CHAPTER 1. THE DIRAC DELTA FUNCTION AND DELTA SEQUENCES; 1.1 The Heaviside Function; 1.2 The Dirac Delta Function; 1.3 The Delta Sequences; 1.4 A Unit Dipole; 1.5 The Heaviside Sequences; Exercises; CHAPTER 2. THE SCHWRTZ-SOBOLEV THEORY OF DISTRIBUTIONS; 2.1 Some Introductory Definitions; 2.2 Test Functions; 2.3 Linear Functionals and the Schwartz-Sobolev Theory of Distributions; 2.4 Examples; 2.5 Algebraic Operations on Distributions; 2.6 Analytic Operations on Distributions; 2.7 Examples
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|a Includes bibliographical references and index
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|a CHAPTER 5. DISTRIBUTIONAL DERIVATIVES OF FUNCTIONS WITH JUMP DISCONTINUITIES5.1 Distributional Derivatives in R1; 5.2 Rn, n = 2; Moving Surfaces of Discontinuity; 5.3 Surface Distributions; 5.4 Various Other Representations; 5.5 First-Order Distributional Derivatives; 5.6 Second-Order Distributional Derivatives; 5.7 Higher-Order Distributional Derivatives; 5.8 The Two-Dimensional Case; 5.9 Examples; CHAPTER 6. TEMPERED DISTRIBUTIONS AND THE FOURIER TRANSFORMS; 6.1 Preliminary Concepts; 6.2 Distributions of Slow Growth (Tempered Distributions); 6.3 The Fourier Transform; 6.4 Examples
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|a 2.8 The Support and Singular Support of a Distribution Exercises; CHAPTER 3. ADDITIONAL PROPERTIES OF DISTRIBUTIONS; 3.1 Transformation Properties of the Delta Distribution; 3.2 Convergence of Distributions; 3.3 Delta Sequences with Parametric Dependence; 3.4 Fourier Series; 3.5 Examples; 3.6 The Delta Function as a Stieltjes Integral; Exercises; CHAPTER 4. DISTRIBUTIONS DEFINED BY DIVERGENT INTEGRALS; 4.1 Introduction; 4.2 The Pseudofunction H(x)/xn, n = 1, 2, 3, . . .; 4.3 Functions with Algebraic Singularity of Order m; 4.4 Examples; Exercises
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|a ExercisesCHAPTER 7. DIRECT PRODUCTS AND CONVOLUTIONS OF DISTRIBUTIONS; 7.1 Definition of the Direct Product; 7.2 The Direct Product of Tempered Distributions; 7.3 The Fourier Transform of the Direct Product of Tempered Distributions; 7.4 The Convolution; 7.5 The Role of Convolution in the Regularization of the Distributions; 7.6 Examples; 7.7 The Fourier Transform of the Convolution; Exercises; CHAPTER 8. THE LAPLACE TRANSFORM; 8.1 A Brief Discussion of the Classical Results; 8.2 The Laplace Transform of Distributions
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|a 8.3 The Laplace Transform of the Distributional Derivatives and Vice Versa8.4 Examples; Exercises; CHAPTER 9. APPLICATIONS TO ORDINARY DIFFERENTIAL EQUATIONS; 9.1 Ordinary Differential Operators; 9.2 Homogeneous Differential Equations; 9.3 Inhomogeneous Differential Equations: The Integral of a Distribution; 9.4 Examples; 9.5 Fundamental Solutions and Green's Functions; 9.6 Second-Order Differential Equations with Constant Coefficients; 9.7 Eigenvalue Problems; 9.8 Second-Order Differential Equations with Variable Coefficients; 9.9 Fourth-Order Differential Equations
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| 653 |
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|a Théorie des distributions (Analyse fonctionnelle)
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| 653 |
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|a Theory of distributions (Functional analysis) / fast / (OCoLC)fst01149672
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| 653 |
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|a MATHEMATICS / Functional Analysis / bisacsh
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| 653 |
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|a Theory of distributions (Functional analysis) / http://id.loc.gov/authorities/subjects/sh85038549
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|a eng
|2 ISO 639-2
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| 989 |
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|b ZDB-1-ELC
|a Elsevier eBook collection Mathematics
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| 490 |
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|a Mathematics in science and engineering
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| 776 |
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|z 9780080956763
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| 776 |
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|z 0080956769
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| 776 |
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|z 9780123965608
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| 776 |
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|z 0123965608
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| 856 |
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|u https://www.sciencedirect.com/science/bookseries/00765392/171
|x Verlag
|3 Volltext
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| 082 |
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|a 515.7/223
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| 520 |
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|a Generalized functions : theory and technique
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