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Generalized Functions Theory and Applications

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ISBN-10: 0817643435

ISBN-13: 9780817643430

Edition: 3rd 2004 (Revised)

Authors: Ram P. Kanwal

List price: $109.99
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Description:

This third edition of "Generalized Functions" expands the treatment of fundamental concepts and theoretical background material and delineates connections to a variety of applications in mathematical physics, elasticity, wave propagation, magnetohydrodynamics, linear systems, probability and statistics, optimal control problems in economics, and more. In applying the powerful tools of generalized functions to better serve the needs of physicists, engineers, and applied mathematicians, this work is quite distinct from other books on the subject.Key new topics and important features:* Examination of the Poisson Summation Formula and the concepts of differential forms and the delta…    
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Book details

List price: $109.99
Edition: 3rd
Copyright year: 2004
Publisher: Birkh�user Boston
Publication date: 7/23/2004
Binding: Paperback
Pages: 476
Size: 7.01" wide x 10.00" long x 1.00" tall
Weight: 2.068

Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
The Dirac Delta Function and Delta Sequences
The Heaviside Function
The Dirac Delta Function
The Delta Sequences
A Unit Dipole
The Heaviside Sequences
Exercises
The Schwartz-Sobolev Theory of Distributions
Some Introductory Definitions
Test Functions
Linear Functionals and the Schwartz Sobolev Theory of Distributions
Examples
Algebraic Operations on Distributions
Analytic Operations on Distributions
Examples
The Support and Singular Support of a Distribution Exercises
Additional Properties of Distributions
Transformation Properties of the Delta Distributions
Convergence of Distributions
Delta Sequences with Parametric Dependence
Fourier Series
Examples
The Delta Function as a Stieltjes Integral Exercises
Distributions Defined by Divergent Integrals
Introduction
The Pseudofunction H(x)/x n , n = 1, 2,3
Functions with Algebraic Singularity of Order m
Examples
Exercises
Distributional Derivatives of Functions with Jump Discontinuities
Distributional Derivatives in R 1
Moving Surfaces of Discontinuity in R n , n 2
Surface Distributions
Various Other Representations
First-Order Distributional Derivatives
Second Order Distributional Derivatives
Higher-Order Distributional Derivatives
The Two-Dimensional Case
Examples
The Function Pf ( l/r ) and its Derivatives
Tempered Distributions and the Fourier Transforms
Preliminary Concepts
Distributions of Slow Growth (Tempered Distributions)
The Fourier Transform
Examples
Exercises
Direct Products and Convolutions of Distributions
Definition of the Direct Product
The Direct Product of Tempered Distributions
The Fourier Transform of the Direct Product of Tempered Distributions
The Convolution
The Role of Convolution in the Regularization of the Distributions
The Dual Spaces E and E''
Examples
The Fourier Transform of the Convolution
Distributional Solutions of Integral Equations
Exercises
The Laplace Transform
A Brief Discussion of the Classical Results
The Laplace Transform of the Distributions
The Laplace Transform of the Distributional Derivatives and Vice Versa
Examples
Exercises
Applications to Ordinary Differential Equations
Ordinary Differential Operators
Homogeneous Differential Equations
Inhomogeneous Differentational Equations: The Integral of a Distribution
Examples
Fundamental Solutions and Green''s Functions
Second Order Differential Equations with Constant Coefficients
Eigenvalue Problems
Second Order Differential Equations with Variable Coefficients
Fourth Order Differential Equations
Differential Equations of n th Order
Ordinary Differential Equations with Singular Coefficients
Exercises
Applications to Partial Differential Equations
Introduction
Classical and Generalized Solutions
Fundamental Solutions
The Cauchy Riemann Operator
The Transport Operator
The Laplace Operator
The Heat Operator
The Schroedinger Operator
The Helmholtz Operator
The Wave Operator
The Inhomogeneous Wave Equation
The Klein Gordon Operator
Exercises
Applications to Boundary Value Problems
Poisson''s Equation
Dumbbell-Shaped Bodies
Uniform Axial Distributions
Linear Axial Distributions
Parabolic Axial Distributions
The Four-Order Polynomial Distribution, n = 7
Spheroidal Cavities
The Polarization Tensor for a Spheroid
The Virtual Mass Tensor for a Sp