Generalized Functions Volume 2 Spaces Of Fundamental And Generalized Functions
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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 Spaces Of Fundamental And Generalized Functions
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Author : Izrailʹ Moiseevich Gelʹfand
language : en
Publisher:
Release Date :
Generalized Functions Spaces Of Fundamental And 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 with Theory of distributions (Functional analysis) categories.
Generalized Functions Volume 2 Spaces Of Fundamental And Generalized Functions
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Author : I. M. Gel'fand
language : en
Publisher:
Release Date : 1968
Generalized Functions Volume 2 Spaces Of Fundamental And Generalized Functions 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 1968 with categories.
Spaces Of Fundamental And Generalized Functions
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Author : I. M. Gel'Fand
language : en
Publisher: Academic Press
Release Date : 2013-09-03
Spaces Of Fundamental And 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 2013-09-03 with Mathematics categories.
Spaces of Fundamental and Generalized Functions, Volume 2, analyzes the general theory of linear topological spaces. The basis of the theory of generalized functions is the theory of the so-called countably normed spaces (with compatible norms), their unions (inductive limits), and also of the spaces conjugate to the countably normed ones or their unions. This set of spaces is sufficiently broad on the one hand, and sufficiently convenient for the analyst on the other. The book opens with a chapter that discusses the theory of these spaces. This is followed by separate chapters on fundamental and generalized functions, Fourier transformations of fundamental and generalized functions, and spaces of type S.
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
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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.
P Adic Analysis
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Author : W. A. Zúñiga-Galindo
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-12-02
P Adic Analysis written by W. A. Zúñiga-Galindo and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-02 with Mathematics categories.
This book is intended to provide a fast, interdisciplinary introduction to the basic results of p-adic analysis and its connections with mathematical physics and applications. The book revolves around three topics: (1) p-adic heat equations and ultradiffusion; (2) fundamental solutions and local zeta functions, Riesz kernels, and quadratic forms; (3) Sobolev-type spaces and pseudo-differential evolution equations. These topics are deeply connected with very relevant current research areas. The book includes numerous examples, exercises, and snapshots of several mathematical theories. This book arose from the need to quickly introduce mathematical audience the basic concepts and techniques to do research in p-adic analysis and its connections with mathematical physics and other areas. The book is addressed to a general mathematical audience, which includes computer scientists, theoretical physicists, and people interested in mathematical analysis, PDEs, etc.
Fractional Integrals Potentials And Radon Transforms
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Author : Boris Rubin
language : en
Publisher: CRC Press
Release Date : 2024-08-14
Fractional Integrals Potentials And Radon Transforms written by Boris Rubin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-14 with Mathematics categories.
Fractional Integrals, Potentials, and Radon Transforms, Second Edition presents recent developments in the fractional calculus of functions of one and several real variables, and shows the relation of this field to a variety of areas in pure and applied mathematics. In this thoroughly revised new edition, the book aims to explore how fractional integrals occur in the study of diverse Radon type transforms in integral geometry. Beyond some basic properties of fractional integrals in one and many dimensions, this book also contains a mathematical theory of certain important weakly singular integral equations of the first kind arising in mechanics, diffraction theory and other areas of mathematical physics. The author focuses on explicit inversion formulae that can be obtained by making use of the classical Marchaud’s approach and its generalization, leading to wavelet type representations. New to this Edition Two new chapters and a new appendix, related to Radon transforms and harmonic analysis of linear operators commuting with rotations and dilations have been added. Contains new exercises and bibliographical notes along with a thoroughly expanded list of references. This book is suitable for mathematical physicists and pure mathematicians researching in the area of integral equations, integral transforms, and related harmonic analysis.
Conceptual Tools For Understanding Nature Proceedings Of The International Symposium
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Author : Giacomo Costa
language : en
Publisher: World Scientific
Release Date : 1993-12-17
Conceptual Tools For Understanding Nature Proceedings Of The International Symposium written by Giacomo Costa and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-17 with categories.
This symposium is the first scientific event organized by the “Seminar for Epistemology” under the auspices of the University of Trieste. The aim of the symposium was to collect and open to discussion the contributions of a number of distinguished scientists from cognitive sciences and experimental nature sciences and to bring together specialists of various backgrounds.The very authoritative contributions presented at the Conference represent relevant, even if not exhaustive, specimens of the role of new conceptual tools in science.
An Introduction To Sparse Stochastic Processes
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Author : Michael Unser
language : en
Publisher: Cambridge University Press
Release Date : 2014-08-21
An Introduction To Sparse Stochastic Processes written by Michael Unser and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-21 with Computers categories.
A detailed guide to sparsity, providing a description of their transform-domain statistics and applying the models to practical algorithms.