Generalized Functions Volume 3 Theory Of Differential Equations
DOWNLOAD
Download Generalized Functions Volume 3 Theory Of Differential Equations PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Generalized Functions Volume 3 Theory Of Differential Equations book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Generalized Functions Volume 3
DOWNLOAD
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.
Theory Of Differential Equations
DOWNLOAD
Author : I. M. Gel'fand
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Theory Of Differential Equations 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 3: Theory of Differential Equations focuses on the application of generalized functions to problems of the theory of partial differential equations. This book discusses the problems of determining uniqueness and correctness classes for solutions of the Cauchy problem for systems with constant coefficients and eigenfunction expansions for self-adjoint differential operators. The topics covered include the bounded operators in spaces of type W, Cauchy problem in a topological vector space, and theorem of the Phragmén-Lindelöf type. The correctness classes for the Cauchy problem, systems that are Petrovski?-correct, and generalized eigenfunctions of self-adjoint operators are also reviewed. This text likewise covers the differentiation of functionals of strongly and weakly bounded variation. This volume is beneficial to students and researchers interested in the theory of differential equations.
Generalized Functions Theory And Technique
DOWNLOAD
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 3 Theory Of Differential Equations
DOWNLOAD
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.
Generalized Functions
DOWNLOAD
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.
Generalized Functions And Partial Differential Equations
DOWNLOAD
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 2
DOWNLOAD
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 3 Theory Of Differential Equations
DOWNLOAD
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.
Spaces Of Fundamental And Generalized Functions
DOWNLOAD
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
DOWNLOAD
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.