Distributions : generalized functions with applications in Sobolev spaces / Pulin Kumar Bhattacharyya.

Includes bibliographical references and index.

This book grew out of a course taught in the Department of Mathematics, Indian Institute of Technology, Delhi, which was tailored to the needs of the applied community of mathematicians, engineers, physicists etc., who were interested in studying the problems of mathematical physics in general and their approximate solutions on computer in particular. Almost all topics which will be essential for the study of Sobolev spaces and their applications in the elliptic boundary value problems and their finite element approximations are presented. Also many additional topics of interests for specific applied disciplines and engineering, for example, elementary solutions, derivatives of discontinuous functions of several variables, delta-convergent sequences of functions, Fourier series of distributions, convolution system of equations etc. have been included along with many interesting examples.

In English.

880-01 Preface ; How to use this book in courses ; Acknowledgment ; Notation ; 1 Schwartz distributions ; 1.1 Introduction: Dirac's delta function e(x) and its properties ; 1.2 Test space D (]) of Schwartz ; 1.2.1 Support of a continuous function ; 1.2.2 Space D (]) ; 1.2.3 Space Dm(]); 1.2.4 Space DK (]) ; 1.2.5 Properties of D (]) ; 1.3 Space D'(]) of (Schwartz) distributions; 1.3.1 Algebraic dual space D*(]).

1.3.2 Distributions and the space D'(]) of distributions on ]1.3.3 Characterization, order and extension of a distribution ; 1.3.4 Examples of distributions ; 1.3.5 Distribution defined on test space D(]) of complex-valued functions ; 1.4 Some more examples of interesting distributions ; 1.5 Multiplication of distributions by C -functions ; 1.6 Problem of division of distributions.

1.7 Even, odd and positive distributions 1.8 Convergence of sequences of distributions in D'(]); 1.9 Convergence of series of distributions in D'(]) ; 1.10 Images of distributions due to change of variables, homogeneous, invariant, spherically symmetric, constant distributions ; 1.10.1 Periodic distributions.

1.11 Physical distributions versus mathematical distributions 1.11.1 Physical interpretation of mathematical distributions ; 1.11.2 Load intensity ; 1.11.3 Electrical charge distribution ; 1.11.4 Simple layer and double layer distributions.

1.11.5 Relation with probability distribution [7] 2 Differentiation of distributions and application of distributional derivatives ; 2.1 Introduction: an integral definition of derivatives of C1-functions ; 2.2 Derivatives of distributions.

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