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In the second of six volumes on the theory of generalized functions, Gel'fand and Silov demonstrate the fundamental peculiarity of the theory of the generalized functions in that different classes of problems require different classes of spaces--not just different spaces, but different classes of spaces. They cover linear topological spaces, fundamental and generalized functions, Fourier transformations of fundamental and generalized functions, and spaces of type S. Detailed topics include continuous linear operators, the structure of generalized functions, Fourier transformations of entire analytic functions, and the question of the non-triviality of spaces of type S. Annotation ©2016 Ringgold, Inc., Portland, OR (protoview.com)
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Generalized Functions : Spaces of Fundamental and Generalized Functions
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American Mathematical Society, 2016
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Generalized Functions, Volume 2
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Generalized Functions, Volume 2
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Hardback. Condizione: New. 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. Gelfand 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. Codice articolo LU-9781470426590
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Generalized Functions : Spaces of Fundamental and Generalized Functions
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Generalized Functions : Spaces of Fundamental and Generalized Functions
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Gel\ Fand, I: Generalized Functions, Volume 2
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Condizione: New. The six-volume collection, Generalized Functions, 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 dev. Codice articolo 595975058
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Generalized Functions, Volume 2
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American Mathematical Society, 2016
ISBN 10: 1470426595
ISBN 13: 9781470426590
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Hardback. Condizione: New. 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. Gelfand 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. Codice articolo LU-9781470426590
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