Dieudonne J. (EN) — History of Functional Analysis

Тут можно читать онлайн книгу Dieudonne J. (EN) - History of Functional Analysis - бесплатно полную версию (целиком). Жанр книги: Иностранная литература. Вы можете прочесть полную версию (весь текст) онлайн без регистрации и смс на сайте Lib-King.Ru (Либ-Кинг) или прочитать краткое содержание, аннотацию (предисловие), описание и ознакомиться с отзывами (комментариями) о произведении.

History of Functional Analysis
Язык книги: Английский
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History of Functional Analysis краткое содержание

History of Functional Analysis - описание и краткое содержание, автор Dieudonne J. (EN), читать бесплатно онлайн на сайте электронной библиотеки Lib-King.Ru.

History of Functional Analysis presents functional analysis as a rather complex blend of algebra and topology, with its evolution influenced by the development of these two branches of mathematics. The book adopts a narrower definition-one that is assumed to satisfy various algebraic and topological conditions. A moment of reflections shows that this already covers a large part of modern analysis, in particular, the theory of partial differential equations. This volume comprises nine chapters, the first of which focuses on linear differential equations and the Sturm-Liouville problem. The succeeding chapters go on to discuss the "crypto-integral" equations, including the Dirichlet principle and the Beer-Neumann method; the equation of vibrating membranes, including the contributions of Poincare and H.A. Schwarz's 1885 paper; and the idea of infinite dimension. Other chapters cover the crucial years and the definition of Hilbert space, including Fredholm's discovery and the contributions of Hilbert; duality and the definition of normed spaces, including the Hahn-Banach theorem and the method of the gliding hump and Baire category; spectral theory after 1900, including the theories and works of F. Riesz, Hilbert, von Neumann, Weyl, and Carleman; locally convex spaces and the theory of distributions; and applications of functional analysis to differential and partial differential equations. This book will be of interest to practitioners in the fields of mathematics and statistics.

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