000			03108nam a22003137a 4500
003			OSt
005			20240517185235.0
008			240517b |||||||| |||| 00| 0 hin d
020			_a9781470426637
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 5 : _bintegral geometry and representation theory
260			_aProvidence, Rhode Island : _bAmerican Mathematical Society Chelsea Publishing, _c2016.
300			_axvii, 449p. : _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 unifying idea of Volume 5 in the series is the application of the theory of generalized functions developed in earlier volumes to problems of integral geometry, to representations of Lie groups, specifically of the Lorentz group, and to harmonic analysis on corresponding homogeneous spaces. The book is written with great clarity and requires little in the way of special previous knowledge of either group representation theory or integral geometry; it is also independent of the earlier volumes in the series. The exposition starts with the definition, properties, and main results related to the classical Radon transform, passing to integral geometry in complex space, representations of the group of complex unimodular matrices of second order, and harmonic analysis on this group and on most important homogeneous spaces related to this group. The volume ends with the study of representations of the group of real unimodular matrices of order two.
521			_aGraduate students and research mathematicians interested in integral geometry and representation theory.
650		0	_aTheory of distributions (Functional analysis)
650		0	_aFunctional analysis -- Distributions, generalized functions, distribution spaces -- Distributions, generalized functions, distribution spaces
650		0	_aIntegral geometry
700	1		_aGraev, M. I. _q(Mark Iosifovich)
700	1		_aVilenkin, N, Ya. _q(Naum I︠A︡kovlevich)
856			_3Table of Contents _uhttps://www.ams.org/bookstore/pspdf/chel-381-h-toc.pdf?_gl=1*3o2xxs*_ga*MTg3NTQ1NzY3LjE3MTEwOTIxMzU.*_ga_26G4XFTR63*MTcxNTk0NDY2MC41LjEuMTcxNTk1MjEyMC4wLjAuMA..
856			_3Reviews _uhttps://www.goodreads.com/book/show/29445002-generalized-functions?ref=nav_sb_ss_1_13#CommunityReviews
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