Generalized Functions: Applications of Harmonic Analysis

by Israel M. Gelfand, Naum Yakovlevich Vilenkin

Generalized Functions, Volume 4: Applications of Harmonic Analysis is devoted to two general topics—developments in the theory of linear topological spaces and construction of harmonic analysis in n-dimensional Euclidean and infinite-dimensional spaces. This volume specifically discusses the bilinear functionals on countably normed spaces, Hilbert-Schmidt operators, and spectral analysis of operators in rigged Hilbert spaces. The general form of positive generalized functions on the space S, continuous positive-definite functions, and conditionally positive generalized functions are also deliberated. This publication likewise considers the mean of a generalized random process, multidimensional generalized random fields, simplest properties of cylinder sets, and definition of Gaussian measures. This book is beneficial to students, specialists, and researchers aiming to acquire knowledge of functional analysis.

Genres: Mathematics

398 pages, Kindle Edition

Published May 12, 2014

About the author

Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand (Yiddish: ישראל געלפֿאַנד‎, Russian: Израиль Моисеевич Гельфанд ; 2 September [O.S. 20 August] 1913 – 5 October 2009) was a prominent Soviet mathematician. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis. The recipient of many awards, including the Order of Lenin and the Wolf Prize, he was a Fellow of the Royal Society and professor at Moscow State University and, after immigrating to the United States shortly before his 76th birthday, at Rutgers University.