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Methods of the Theory of Generalized Functions

2002-08-15 Mathematics
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Release : 2002-08-15
Genre : Mathematics
Kind : eBook
Book Rating : 565/5 ( reviews)

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Book Synopsis Methods of the Theory of Generalized Functions by : V. S. Vladimirov

Download or read book Methods of the Theory of Generalized Functions written by V. S. Vladimirov. This book was released on 2002-08-15. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the general theory of generalized functions, including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner and Poisson integral transforms and operational calculus, with the traditional material augmented by the theory of Fourier series, abelian theorems, and boundary values of helomorphic functions for one and several variables. The author addresses several facets in depth, including convolution theory, convolution algebras and convolution equations in them, homogenous generalized functions, and multiplication of generalized functions. This book will meet the needs of researchers, engineers, and students of applied mathematics, control theory, and the engineering sciences.

Generalized Functions Theory and Technique

1998-01-01 Mathematics
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Release : 1998-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 064/5 ( reviews)

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Book Synopsis Generalized Functions Theory and Technique by : Ram P. Kanwal

Download or read book Generalized Functions Theory and Technique written by Ram P. Kanwal. This book was released on 1998-01-01. Available in PDF, EPUB and Kindle. Book excerpt: This second edition of Generalized Functions has been strengthened in many ways. The already extensive set of examples has been expanded. Since the publication of the first edition, there has been tremendous growth in the subject and I have attempted to incorporate some of these new concepts. Accordingly, almost all the chapters have been revised. The bibliography has been enlarged considerably. Some of the material has been reorganized. For example, Chapters 12 and 13 of the first edition have been consolidated into Chapter 12 of this edition by a judicious process of elimination and addition of the subject matter. The new Chapter 13 explains the interplay between the theories of moments, asymptotics, and singular perturbations. Similarly, some sections of Chapter 15 have been revised and included in earlier chapters to improve the logical flow of ideas. However, two sections are retained. The section dealing with the application of the probability theory has been revised, and I am thankful to Professor Z.L. Crvenkovic for her help. The new material included in this chapter pertains to the modern topics of periodic distributions and microlocal theory. I have demonstrated through various examples that familiarity with the generalized functions is very helpful for students in physical sciences and technology. For instance, the reader will realize from Chapter 6 how the generalized functions have revolutionized the Fourier analysis which is being used extensively in many fields of scientific activity.

Generalized Functions: Theory and Technique

1983-12-01 Computers
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Release : 1983-12-01
Genre : Computers
Kind : eBook
Book Rating : 769/5 ( reviews)

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Book Synopsis Generalized Functions: Theory and Technique by : Kanwal

Download or read book Generalized Functions: Theory and Technique written by Kanwal. This book was released on 1983-12-01. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Functions: Theory and Technique

Methods of the Theory of Generalized Functions of Many Complex Variables

1966
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Release : 1966
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Book Synopsis Methods of the Theory of Generalized Functions of Many Complex Variables by : Vasilij Sergeevič Vladimirov

Download or read book Methods of the Theory of Generalized Functions of Many Complex Variables written by Vasilij Sergeevič Vladimirov. This book was released on 1966. Available in PDF, EPUB and Kindle. Book excerpt:

Generalized Functions, Volume 1

2016-04-19 Mathematics
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Release : 2016-04-19
Genre : Mathematics
Kind : eBook
Book Rating : 587/5 ( reviews)

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Book Synopsis Generalized Functions, Volume 1 by : I. M. Gel′fand

Download or read book Generalized Functions, Volume 1 written by I. M. Gel′fand. This book was released on 2016-04-19. Available in PDF, EPUB and Kindle. Book excerpt: he first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gel′fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. Volume 1 is devoted to basics of the theory of generalized functions. The first chapter contains main definitions and most important properties of generalized functions as functional on the space of smooth functions with compact support. The second chapter talks about the Fourier transform of generalized functions. In Chapter 3, definitions and properties of some important classes of generalized functions are discussed; in particular, generalized functions supported on submanifolds of lower dimension, generalized functions associated with quadratic forms, and homogeneous generalized functions are studied in detail. Many simple basic examples make this book an excellent place for a novice to get acquainted with the theory of generalized functions. A long appendix presents basics of generalized functions of complex variables.

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