Generalized functions : theory and technique /

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Generalized functions : theory and technique.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Kanwal, Ram P.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York : Academic Press, 1983.
Colección:Mathematics in science and engineering ; v. 171.
Temas:
Theory of distributions (Functional analysis)
Th�eorie des distributions (Analyse fonctionnelle)
MATHEMATICS > Functional Analysis.
Acceso en línea:Texto completo
Texto completo
Texto completo

MARC

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100 1 |a Kanwal, Ram P. 
245 1 0 |a Generalized functions :  |b theory and technique /  |c Ram P. Kanwal. 
260 |a New York :  |b Academic Press,  |c 1983. 
300 |a 1 online resource (xiii, 428 pages) :  |b illustrations 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a Mathematics in science and engineering ;  |v v. 171 
504 |a Includes bibliographical references and index. 
588 0 |a Print version record. 
505 0 |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 
505 8 |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 
505 8 |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 
505 8 |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 
505 8 |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 
520 |a Generalized functions : theory and technique. 
650 0 |a Theory of distributions (Functional analysis) 
650 6 |a Th�eorie des distributions (Analyse fonctionnelle)  |0 (CaQQLa)201-0058588 
650 7 |a MATHEMATICS  |x Functional Analysis.  |2 bisacsh 
650 7 |a Theory of distributions (Functional analysis)  |2 fast  |0 (OCoLC)fst01149672 
776 0 8 |i Print version:  |a Kanwal, Ram P.  |t Generalized functions.  |d New York : Academic Press, 1983  |z 9780123965608  |w (DLC) 83002617  |w (OCoLC)10268198 
830 0 |a Mathematics in science and engineering ;  |v v. 171. 
856 4 0 |u https://sciencedirect.uam.elogim.com/science/book/9780123965608  |z Texto completo 
856 4 0 |u https://sciencedirect.uam.elogim.com/science/publication?issn=00765392&volume=171  |z Texto completo 
856 4 0 |u https://sciencedirect.uam.elogim.com/science/bookseries/00765392/171  |z Texto completo 

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