000			03015cam a2200313 i 4500
003			OSt
005			20240517165730.0
008			151013r20161964riu b 001 0 eng
020			_a9781470426583
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)
240			_aObobshchennye funkt︠s︡ii. _lEnglish
245	1	0	_aGeneralized functions, volume 1 : _bproperties and operations.
260			_aProvidence, Rhode Island : _bAmerican Mathematical Society Chelsea Publishing, _c2016.
300			_axviii, 423p. : _billustrations (black and white) ; _c26 cm.
500			_aOriginally published in Russian in 1958.
500			_aOriginally published in English as 5 volume set: New York : Academic Press, 1964-[1968].
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. Volume 1 is devoted to basics of the theory of generalized functions. The first chapter contains main definitions and most important properties of generalized functions as functional on the space of smooth functions with compact support. The second chapter talks about the Fourier transform of generalized functions. In Chapter 3, definitions and properties of some important classes of generalized functions are discussed; in particular, generalized functions supported on submanifolds of lower dimension, generalized functions associated with quadratic forms, and homogeneous generalized functions are studied in detail. Many simple basic examples make this book an excellent place for a novice to get acquainted with the theory of generalized functions. A long appendix presents basics of generalized functions of complex variables.
650			_aTheory of distributions (Functional analysis)
650			_aFunctional analysis -- Distributions, generalized functions, distribution spaces -- Distributions, generalized functions, distribution spaces.
700	1		_aShilov, G. E. _q(Georgiĭ Evgenʹevich)
856			_3Table of Contents _uhttps://www.ams.org/bookstore/pspdf/chel-377-h-toc.pdf?_gl=1*1d8aj54*_ga*MTg3NTQ1NzY3LjE3MTEwOTIxMzU.*_ga_26G4XFTR63*MTcxNTk0NDY2MC41LjEuMTcxNTk0NTAyMS4wLjAuMA..
856			_3Reviews _uhttps://www.goodreads.com/book/show/148442360-generalized-functions?from_search=true&from_srp=true&qid=lCl9Qf8Uo7&rank=1#CommunityReviews
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