000			02853nam a22003257a 4500
003			OSt
005			20240517182834.0
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020			_a9781470426620
020			_a9781470428853
040			_aNISER LIBRARY _beng _cNISER LIBRARY
041	1		_aEnglish
082	0	0	_a517.98 _bGEL-G
100	1		_aGelʹfand, I. M. _q(Izrailʹ Moiseevich)
245	1	0	_aGeneralized functions, volume 4 : _bapplications of harmonic analysis.
260			_aProvidence, Rhode Island : _bAmerican Mathematical Society Chelsea Publishing, _c2016.
300			_axiv, 384p. : _billustrations (black and white) ; _c26 cm.
504			_aIncludes bibliographical references and index.
520			_aThe 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. Gel′fand 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⊂H⊂E′, where H is a Hilbert space, E′ is dual to E, and inclusions E⊂H and H⊂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.
521			_aGraduate students and research mathematicians interested in functional analysis.
650		0	_aTheory of distributions (Functional analysis)
650		0	_aFunctional analysis -- Distributions, generalized functions, distribution spaces -- Distributions, generalized functions, distribution spaces
650		0	_aHarmonic analysis
650		0	_aMathematics _xCalculus.
650		0	_aMathematics _xMathematical Analysis
700	1		_aVilenkin, N. Ya. _q(Naum I︠A︡kovlevich)
856			_3Table of Contents _uhttps://www.ams.org/bookstore/pspdf/chel-380-h-toc.pdf?_gl=1*w2pf86*_ga*MTg3NTQ1NzY3LjE3MTEwOTIxMzU.*_ga_26G4XFTR63*MTcxNTk0NDY2MC41LjEuMTcxNTk0OTcxMy4wLjAuMA..
856			_3Reviews _uhttps://www.goodreads.com/book/show/29445001-generalized-functions?from_search=true&from_srp=true&qid=R0B2teQbkE&rank=1#CommunityReviews
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