000			03143nam a22003497a 4500
003			OSt
005			20240517172545.0
008			240517b |||||||| |||| 00| 0 hin d
020			_a9781470426590
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 2 : _bspaces of fundamental and generalized functions.
260			_aProvidence, Rhode Island : _bAmerican Mathematical Society Chelsea Publishing, _c2016.
300			_ax, 261p. : _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. Volume 2 is devoted to detailed study of generalized functions as linear functionals on appropriate spaces of smooth test functions. In Chapter 1, the authors introduce and study countable-normed linear topological spaces, laying out a general theoretical foundation for the analysis of spaces of generalized functions. The two most important classes of spaces of test functions are spaces of compactly supported functions and Schwartz spaces of rapidly decreasing functions. In Chapters 2 and 3 of the book, the authors transfer many results presented in Volume 1 to generalized functions corresponding to these more general spaces. Finally, Chapter 4 is devoted to the study of the Fourier transform; in particular, it includes appropriate versions of the Paley–Wiener theorem.
521			_aGraduate students and research mathematicians interested in analysis and differential equations.
650		0	_aTheory of distributions (Functional analysis)
650		0	_aFunctional analysis -- Distributions, generalized functions, distribution spaces -- Distributions, generalized functions, distribution spaces
650		0	_aFunctional analysis _xNumerical solutions.
650		0	_aFunctional equations _xNumerical solutions.
650		0	_aMathematics _xCalculus
650		0	_aMathematics _xMathematical Analysis
700	1		_aShilov, G. E. _q(Georgiĭ Evgenʹevich)
856			_3Table of Contents _uhttps://www.ams.org/bookstore/pspdf/chel-378-h-toc.pdf?_gl=1*15xj5hz*_ga*MTg3NTQ1NzY3LjE3MTEwOTIxMzU.*_ga_26G4XFTR63*MTcxNTk0NDY2MC41LjEuMTcxNTk0NTU5OC4wLjAuMA..
856			_3Reviews _uhttps://www.goodreads.com/book/show/29444999-generalized-functions-volume-2?from_search=true&from_srp=true&qid=FAs6fCsF3o&rank=1#CommunityReviews
942			_cBK _2udc
999			_c34999 _d34999