Generalized Functions Theory And Technique

Author : Ram P. Kanwal
Publisher : Springer Science & Business Media
ISBN 13 : 9780817640064
Total Pages : 478 pages
Book Rating : 4.61/5 ( download)

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Download or read book Generalized Functions Theory and Technique written by Ram P. Kanwal and published by Springer Science & Business Media. This book was released on 1998-01-01 with total page 478 pages. 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.

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.74/5 ( download)

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Download or read book Generalized Functions written by and published by . This book was released on 1967 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Ram P. Kanwal
Publisher : Springer Science & Business Media
ISBN 13 : 0817681744
Total Pages : 490 pages
Book Rating : 4.46/5 ( download)

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Download or read book Generalized Functions written by Ram P. Kanwal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a more cohesive and sharply focused treatment of fundamental concepts and theoretical background material, with particular attention given to better delineating connections to varying applications Exposition driven by additional examples and exercises

Author : Izrailʹ M. Gelʹfand
Publisher :
ISBN 13 :
Total Pages : 222 pages
Book Rating : 4.31/5 ( download)

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Download or read book Generalized Functions written by Izrailʹ M. Gelʹfand and published by . This book was released on 1972 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : V. S. Vladimirov
Publisher : CRC Press
ISBN 13 : 9780415273565
Total Pages : 332 pages
Book Rating : 4.60/5 ( download)

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Download or read book Methods of the Theory of Generalized Functions written by V. S. Vladimirov and published by CRC Press. This book was released on 2002-08-15 with total page 332 pages. 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.

Author : I. M. Gel′fand
Publisher : American Mathematical Soc.
ISBN 13 : 1470426587
Total Pages : 450 pages
Book Rating : 4.83/5 ( download)

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Download or read book Generalized Functions, Volume 1 written by I. M. Gel′fand and published by American Mathematical Soc.. This book was released on 2016-04-19 with total page 450 pages. 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.

Author : Ram P. Kanwal
Publisher : Springer Science & Business Media
ISBN 13 : 1468400355
Total Pages : 474 pages
Book Rating : 4.59/5 ( download)

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Download or read book Generalized Functions Theory and Technique written by Ram P. Kanwal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 474 pages. 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.

Author : Kanwal
Publisher : Academic Press
ISBN 13 : 0080956769
Total Pages : 427 pages
Book Rating : 4.63/5 ( download)

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Download or read book Generalized Functions: Theory and Technique written by Kanwal and published by Academic Press. This book was released on 1983-12-01 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Functions: Theory and Technique

Author : Hebe de Azevedo Biagioni
Publisher : Springer
ISBN 13 : 3540469818
Total Pages : 226 pages
Book Rating : 4.10/5 ( download)

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Download or read book A Nonlinear Theory of Generalized Functions written by Hebe de Azevedo Biagioni and published by Springer. This book was released on 2006-11-14 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applications are not dissociated it may also be useful for physicists and engineers. The needed prerequisites for its reading are essentially reduced to the classical notions of differential calculus and the theory of integration over n-dimensional euclidean spaces.

Author : Izrailʹ Moiseevich Gelʹfand
Publisher :
ISBN 13 : 9781483229775
Total Pages : 272 pages
Book Rating : 4.77/5 ( download)

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Download or read book Generalized Functions written by Izrailʹ Moiseevich Gelʹfand and published by . This book was released on 1968 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: