Generalized Functions 3 Theory Of Differential Equations
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Generalized Functions Theory And Technique
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Author : Ram P. Kanwal
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-01-01
Generalized Functions Theory And Technique written by Ram P. Kanwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
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 3 Theory Of Differential Equations
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Author : Izrailʹ M. Gelʹfand
language : en
Publisher:
Release Date : 1967
Generalized Functions 3 Theory Of Differential Equations written by Izrailʹ M. Gelʹfand and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Theory of distributions (Functional analysis) categories.
Generalized Functions Volume 3
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Author : I. M. Gel'fand
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-03-30
Generalized Functions Volume 3 written by I. M. Gel'fand and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-30 with Mathematics categories.
The 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. In Volume 3, applications of generalized functions to the Cauchy problem for systems of partial differential equations with constant coefficients are considered. The book includes the study of uniqueness classes of solutions of the Cauchy problem and the study of classes of functions where the Cauchy problem is well posed. The last chapter of this volume presents results related to spectral decomposition of differential operators related to generalized eigenfunctions.
Generalized Functions And Partial Differential Equations
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Author : Avner Friedman
language : en
Publisher: Courier Corporation
Release Date : 2011-11-30
Generalized Functions And Partial Differential Equations written by Avner Friedman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with Mathematics categories.
This self-contained text details developments in the theory of generalized functions and the theory of distributions, and it systematically applies them to a variety of problems in partial differential equations. 1963 edition.
Generalized Functions Theory Of Differential Equations By I M Gel Fand And G E Shilov
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Author : Izrailʹ Moiseevich Gelʹfand
language : en
Publisher:
Release Date : 1964
Generalized Functions Theory Of Differential Equations By I M Gel Fand And G E Shilov written by Izrailʹ Moiseevich Gelʹfand and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Functions categories.
Generalized Functions Vol 3
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Author : Izrail Moiseevic Gelfand
language : en
Publisher:
Release Date : 1967
Generalized Functions Vol 3 written by Izrail Moiseevic Gelfand and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
Generalized Functions And Their Applications
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Author : R.S. Pathak
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Generalized Functions And Their Applications written by R.S. Pathak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Social Science categories.
The International Symposium on Generalized Functions and Their Applications was organized by the Department of Mathematics, Banaras Hindu University, and held December 23-26, 1991, on the occasion of the Platinum Jubilee Celebration of the university. More than a hundred mathematicians from ten countries participated in the deliberations of the symposium. Thirty lectures were delivered on a variety of topics within the area. The contributions to the proceedings of the symposium are, with a few exceptions, expanded versions of the lectures delivered by the invited speakers. The survey papers by Komatsu and Hoskins and Sousa Pinto provide an up-to-date account of the theory of hyperfunctions, ultradistributions and microfunctions, and the nonstandard theory of new generalized functions, respectively; those by Stankovic and Kanwal deal with structures and asymptotics. Choquet-Bruhat's work studies generalized functions on manifold and gives applications to shocks and discrete models. The other contributions relate to contemporary problems and achievements in theory and applications, especially in the theory of partial differential equations, differential geometry, mechanics, mathematical physics, and systems science. The proceedings give a very clear impression of the present state of the art in this field and contain many challenges, ideas, and open problems. The volume is very helpful for a broad spectrum of readers: graduate students to mathematical researchers.
A Nonlinear Theory Of Generalized Functions
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Author : Hebe de Azevedo Biagioni
language : en
Publisher: Springer
Release Date : 2006-11-14
A Nonlinear Theory Of Generalized Functions written by Hebe de Azevedo Biagioni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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.
Distribution Theory And Transform Analysis
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Author : A.H. Zemanian
language : en
Publisher: Courier Corporation
Release Date : 2011-11-30
Distribution Theory And Transform Analysis written by A.H. Zemanian and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with Mathematics categories.
Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.
Generalized Functions
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Author : Izrailʹ Moiseevich Gelʹfand
language : en
Publisher:
Release Date : 2016
Generalized Functions written by Izrailʹ Moiseevich Gelʹfand and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Theory of distributions categories.