Download or read book Generalized Functions Spaces of fundamental and generalized functions written by Izrailʹ Moiseevich Gelʹfand and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spaces of fundamental and generalized functions written by Izrailʹ M. Gelʹfand and published by . This book was released on 1972 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Functions Volume 2 written by I. M. Gel'fand and published by American Mathematical Soc.. This book was released on 2016-03-30 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spaces of Fundamental and Generalized Functions written by Izrailʹ Moiseevich Gelʹfand and published by . This book was released on 1968 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spaces of Fundamental and Generalized Functions written by I. M. Gel'Fand and published by Academic Press. This book was released on 2013-09-03 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Generalized Functions written by Izrail Moiseevic Gelfand and published by . This book was released on 1968 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Functions written by and published by . This book was released on 1964 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Functions written by Izrailʹ Moiseevich Gelʹfand and published by . This book was released on 1967 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Functions written by Izrailʹ Moiseevich Gelʹfand and published by . This book was released on 1968 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
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 423 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.
Download or read book Generalized Functions written by Izrailʹ Moiseevich Gelʹfand and published by . This book was released on 1968 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Functions and Partial Differential Equations written by Avner Friedman and published by Courier Corporation. This book was released on 2005-12-10 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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
Download or read book Generalized Functions and Partial Differential Equations written by Avner Friedman and published by Courier Corporation. This book was released on 2011-11-30 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Generalized Functions in Mathematical Physics written by A. S. Demidov and published by Nova Publishers. This book was released on 2001 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book gives an interconnected presentation of some basic ideas, concepts, results of the theory of generalised functions (first of all, in the framework of the theory of distributions) and equations of mathematical physics. A part of the material is given according to the scheme: definition -- theorem -- proof. This scheme is convenient for presenting results in clear and concentrated form. However, it seems reasonable to give a student the possibility not only to study a priori given definitions and proofs of theorems, but also to discover them while considering the problems involved. A series of sections serve this purpose. Moreover, a part of the material is given as exercises and problems.
Download or read book Generalized Functions written by Izrail Moiseevitch Gelfand and published by . This book was released on 1964 with total page 1738 pages. Available in PDF, EPUB and Kindle. Book excerpt:
