I.M. Gel`fand, G.E. Shilov Generalized Functions, Volume 2: Spaces of Fundamental and Generalized Functions 9781470426590

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Автор: I.M. Gel`fand, G.E. Shilov
Название: Generalized Functions, Volume 2: Spaces of Fundamental and Generalized Functions
ISBN: 9781470426590
Издательство: Mare Nostrum (Eurospan)
Классификация:

Основы высшей математики и математический анализ

Функциональный анализ и преобразования

ISBN-10: 1470426595
Обложка/Формат: Hardback
Страницы: 261
Вес: 0.65 кг.
Дата издания: 31.03.2016
Серия: Ams chelsea publishing
Язык: English
Размер: 183 x 262 x 21
Читательская аудитория: Professional and scholarly
Ключевые слова: Calculus & mathematical analysis
Подзаголовок: Spaces of fundamental and generalized functions
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Поставляется из: Англии
Описание: 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 Greens 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.
Дополнительное описание: Calculus and mathematical analysis

Generalized Functions, Volume 2: Spaces of Fundamental and Generalized Functions, I.M. Gel`fand, G.E. Shilov