Generalized Functions, Vol 4: Applications of Harmonic Analysis

I. M. Gelfand; N. Ya Vilenkin

ISBN 10: 1470426625 / ISBN 13: 9781470426620

Published by AMC Chelsea Publishing, American Mathematical Society, Providence, Rhode Island, 2016

Very little to no wear. Quite clean. 'This is the fourth volume of a series of monographs on functional analysis appearing under the title 'Generalized Functions.' It should not, however, be considered a direct sequel to the preceding volumes. . . This book is devoted to two general topics: recent developments in the theory of linear topological spaces and the construction of harmonic analysis in n-dimensional Euclidean and infinite-dimensional spaces.' xiv+384 pages. AMC Chelsea Publishing reprint. 7.25 x 10.25 inches. Size: 4to - over 9¾ - 12" tall. Seller Inventory # 048174

Synopsis:

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. The main goal of Volume 4 is to develop the functional analysis setup for the universe of generalized functions. The main notion introduced in this volume is the notion of rigged Hilbert space (also known as the equipped Hilbert space, or Gelfand triple). Such space is, in fact, a triple of topological vector spaces $E \subset H \subset E'$, where $H$ is a Hilbert space, $E'$ is dual to $E$, and inclusions $E\subset H$ and $H\subset E'$ are nuclear operators. The book is devoted to various applications of this notion, such as the theory of positive definite generalized functions, the theory of generalized stochastic processes, and the study of measures on linear topological spaces.

Bibliographic Details

Title: Generalized Functions, Vol 4: Applications ...
Publisher: AMC Chelsea Publishing, American Mathematical Society, Providence, Rhode Island
Publication Date: 2016
Binding: Hardcover
Condition: Very Good
Book Type: Book