Generalized Functions Volume 3
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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 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 Volume 2
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Author : I. M. Gel'fand
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-03-30
Generalized Functions Volume 2 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. Volume 2 is devoted to detailed study of generalized functions as linear functionals on appropriate spaces of smooth test functions. In Chapter 1, the authors introduce and study countable-normed linear topological spaces, laying out a general theoretical foundation for the analysis of spaces of generalized functions. The two most important classes of spaces of test functions are spaces of compactly supported functions and Schwartz spaces of rapidly decreasing functions. In Chapters 2 and 3 of the book, the authors transfer many results presented in Volume 1 to generalized functions corresponding to these more general spaces. Finally, Chapter 4 is devoted to the study of the Fourier transform; in particular, it includes appropriate versions of the Paley-Wiener theorem.
Generalized Functions Volume 1
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Author : I. M. Gel′fand
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-04-19
Generalized Functions Volume 1 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 2016-04-19 with Mathematics categories.
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.
Generalized Functions Volume 4
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Author : I. M. Gel′fand
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-04-19
Generalized Functions Volume 4 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 2016-04-19 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. The main goal of Volume 4 is to develop the functional analysis setup for the universe of generalized functions. The main notion introduced in this volume is the notion of rigged Hilbert space (also known as the equipped Hilbert space, or Gelfand triple). Such space is, in fact, a triple of topological vector spaces E⊂H⊂E′, where H is a Hilbert space, E′ is dual to E, and inclusions E⊂H and H⊂E′ are nuclear operators. The book is devoted to various applications of this notion, such as the theory of positive definite generalized functions, the theory of generalized stochastic processes, and the study of measures on linear topological spaces.
Generalized Functions
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Author : I. M. Gel'fand
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Generalized Functions written by I. M. Gel'fand and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Generalized Functions, Volume 4: Applications of Harmonic Analysis is devoted to two general topics—developments in the theory of linear topological spaces and construction of harmonic analysis in n-dimensional Euclidean and infinite-dimensional spaces. This volume specifically discusses the bilinear functionals on countably normed spaces, Hilbert-Schmidt operators, and spectral analysis of operators in rigged Hilbert spaces. The general form of positive generalized functions on the space S, continuous positive-definite functions, and conditionally positive generalized functions are also deliberated. This publication likewise considers the mean of a generalized random process, multidimensional generalized random fields, simplest properties of cylinder sets, and definition of Gaussian measures. This book is beneficial to students, specialists, and researchers aiming to acquire knowledge of functional analysis.
Generalized Functions And Partial Differential Equations
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Author : Avner Friedman
language : en
Publisher: Courier Corporation
Release Date : 2005-12-10
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 2005-12-10 with Mathematics categories.
This self-contained treatment develops the theory of generalized functions and the theory of distributions, and it systematically applies them to solving a variety of problems in partial differential equations. A major portion of the text is based on material included in the books of L. Schwartz, who developed the theory of distributions, and in the books of Gelfand and Shilov, who deal with generalized functions of any class and their use in solving the Cauchy problem. In addition, the author provides applications developed through his own research. Geared toward upper-level undergraduates and graduate students, the text assumes a sound knowledge of both real and complex variables. Familiarity with the basic theory of functional analysis, especially normed spaces, is helpful but not necessary. An introductory chapter features helpful background on topological spaces. Applications to partial differential equations include a treatment of the Cauchy problem, the Goursat problem, fundamental solutions, existence and differentiality of solutions of equations with constants, coefficients, and related topics. Supplementary materials include end-of-chapter problems, bibliographical remarks, and a bibliography.
Generalized Functions Volume 3 Theory Of Differential Equations
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Author : I. M. Gel'fand
language : en
Publisher:
Release Date : 1967
Generalized Functions Volume 3 Theory Of Differential Equations written by I. M. Gel'fand 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.
Handbook Of Function And Generalized Function Transformations
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Author : Ahmed I. Zayed
language : en
Publisher: CRC Press
Release Date : 2019-08-21
Handbook Of Function And Generalized Function Transformations written by Ahmed I. Zayed and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-21 with Mathematics categories.
Function transformations, which include linear integral transformations, are some of the most important mathematical tools for solving problems in all areas of engineering and the physical sciences. They allow one to quickly solve a problem by breaking it down into a series of smaller, more manageable problems. The author has compiled the most important and widely used of these function transforms in applied mathematics and electrical engineering. In addition to classical transforms, newer transforms such as wavelets, Zak, and Radon are included. The book is neither a table of transforms nor a textbook, but it is a source book that provides quick and easy access to the most important properties and formulas of function and generalized function transformations.
Integral Transforms Of Generalized Functions And Their Applications
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Author : Ram Shankar Pathak
language : en
Publisher: Routledge
Release Date : 2017-07-05
Integral Transforms Of Generalized Functions And Their Applications written by Ram Shankar Pathak and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-05 with History categories.
For those who have a background in advanced calculus, elementary topology and functional analysis - from applied mathematicians and engineers to physicists - researchers and graduate students alike - this work provides a comprehensive analysis of the many important integral transforms and renders particular attention to all of the technical aspects of the subject. The author presents the last two decades of research and includes important results from other works.