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Gelfand
''Gelfand'' is a surname meaning "elephant" in the Yiddish language and may refer to: * People: ** Alan Gelfand, the inventor of the ollie, a skateboarding move ** Alan E. Gelfand, a statistician ** Boris Gelfand, a chess grandmaster ** Israel Gelfand, a mathematician, ** Mikhail Gelfand, a molecular biologist and bioinformacisist, a grandson of Israel Gelfand ** Vladimir Gelfand, a Soviet-Jewish writer * Notions in mathematics (named after Israel Gelfand): ** the Gelfand representation, in mathematics, allows a complete characterization of commutative C*-algebras as algebras of continuous complex-valued functions ** the Gelfand–Naimark–Segal construction ** the Gelfand–Naimark theorem ** the Gelfand–Mazur theorem ** a Gelfand pair, a pair (''G'',''K'') consisting of a locally compact unimodular group ''G'' and a compact subgroup ''K'' ** a Gelfand triple, a construction designed to link the distribution (test function) and square-integrable aspects of functional analysis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Israel Gelfand
Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand ( yi, ישראל געלפֿאַנד, russian: Изра́иль Моисе́евич Гельфа́нд, uk, Ізраїль Мойсейович Гельфанд; – 5 October 2009) was a prominent Soviet-American 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 first Wolf Prize, he was a Foreign 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. Gelfand is also a 1994 MacArthur Fellow. His legacy continues through his students, who include Endre Szemerédi, Alexandre Kirillov, Edward Frenkel, Joseph Bernstein, David Kazhdan, as well as his own son, Sergei Gelfand. Early years A native of Khers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gelfand Pair
In mathematics, a Gelfand pair is a pair ''(G,K)'' consisting of a Group (mathematics), group ''G'' and a subgroup ''K'' (called an Euler subgroup of ''G'') that satisfies a certain property on restricted representations. The theory of Gelfand pairs is closely related to the topic of Zonal spherical function, spherical functions in the classical theory of special functions, and to the theory of Riemannian symmetric spaces in differential geometry. Broadly speaking, the theory exists to abstract from these theories their content in terms of harmonic analysis and representation theory. When ''G'' is a finite group the simplest definition is, roughly speaking, that the ''(K,K)''-double cosets in ''G'' commute. More precisely, the Hecke algebra of a finite group, Hecke algebra, the algebra of functions on ''G'' that are invariant under translation on either side by ''K'', should be commutative for the convolution on ''G''. In general, the definition of Gelfand pair is roughly that the r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boris Gelfand
Boris Gelfand ( he, בוריס אברמוביץ' גלפנד; be, Барыс Абрамавіч Гельфанд, Barys Abramavich Hel'fand; russian: Борис Абрамович Гельфанд, Boris Abramovich Gel'fand; born 24 June 1968) is a Soviet-born Israeli chess player. A six-time World Championship candidate (1991, 1994–95, 2002, 2007, 2011, 2013), he won the Chess World Cup 2009 and the 2011 Candidates Tournament, making him challenger for the World Chess Championship 2012. Although the match with defending champion Viswanathan Anand finished level at 6–6, Gelfand lost the deciding rapidplay tiebreak by 2½–1½. Gelfand has won major tournaments at Wijk aan Zee, Tilburg, Moscow, Linares and Dos Hermanas. He has competed in eleven Chess Olympiads and held a place within the top 30 players ranked by FIDE from January 1990 to October 2017. Early years Boris Gelfand was born in Minsk, in the Byelorussian Soviet Socialist Republic, on 24 June 1968 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Gelfand
Vladimir Gelfand (russian: Влади́мир Ната́нович Ге́льфанд) (born March 1, 1923 in the village of Novoarkhanhelsk, Kirovohrad Oblast; died in November 25, 1983 in the city of Dnepropetrovsk, Ukraine) was a diarist and Soviet soldier in World War II. He is known as the author of the diaries from the years 1941–1946 which were published in Germany, Sweden and Russia. The book with the diaries-notices of the officer in the Red Army Vladimir Gelfand: ''German Diary 1945–1946'' ''(Deutschland-Tagebuch 1945–1946)'' – ''Notations of a Soldier in the Red Army'' has become the first one which is published in Germany. Biography Childhood and youth Vladimir Gelfand was the only child in a poor Jewish family. Vladimir’s mother, Nadezhda Vladimirovna Gorodynskaya (1902-1982), was from a low-income family with eight children. In her youth, she earned money by giving private lessons. In 1917, she joined the RSDLP (b) and, as Vladimir mentioned in his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gelfand Representation
In mathematics, the Gelfand representation in functional analysis (named after I. M. Gelfand) is either of two things: * a way of representing commutative Banach algebras as algebras of continuous functions; * the fact that for commutative C*-algebras, this representation is an isometric isomorphism. In the former case, one may regard the Gelfand representation as a far-reaching generalization of the Fourier transform of an integrable function. In the latter case, the Gelfand–Naimark representation theorem is one avenue in the development of spectral theory for normal operators, and generalizes the notion of diagonalizing a normal matrix. Historical remarks One of Gelfand's original applications (and one which historically motivated much of the study of Banach algebras) was to give a much shorter and more conceptual proof of a celebrated lemma of Norbert Wiener (see the citation below), characterizing the elements of the group algebras ''L''1(R) and \ell^1() whose translates s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan Gelfand
Alan "Ollie" Gelfand (born 1963 in New York City) is an American skateboarder and the inventor of the ollie, a skateboarding trick. Life and career Gelfand moved from New York City to Hollywood, Florida with his family in 1972. He started skateboarding in 1974 after his father bought him his first skateboard. In 1976 he won the South Florida Skateboard Championships. That same year the first concrete skateboard parks began to appear in the United States with the first being Skateboard City just up the coast in Port Orange, Florida. In 1977 Hollywood would get its own park called Skateboard USA and it would be here that Gelfand would get his first notice in the skate world. It would be another Hollywood skater by the name of Scott Goodman who would give Gelfand his nickname of "Ollie" and who would name Gelfand's accidental aerial lipslide an Ollie Pop. Skateboard USA with its imperfect walls was atypical of the first-generation skate parks and it was the over-vertical sections o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mikhail Gelfand
Mikhail Sergeyevich Gelfand (russian: Михаил Сергеевич Гельфанд; born 25 October 1963) is a Russian Bioinformaticist and molecular biologist. He is a member of Academia Europaea, Vice President Biomedical Research of Skolkovo Institute of Science and Technology, one of the founder of Dissernet plagiarism fighting society and a political activist, former member of Russian Opposition Coordination Council. He is a grandson of a prominent Soviet mathematician Israel Gelfand. Some works by Mikhail Gelfand * Gelfand M. S. Statistical analysis of mammalian pre-mRNA splicing sites // Nucleic Acids Research. 1989. V. 17. N. 15. 6369—6382. * Gelfand M. S. Computer prediction of the exon-intron structure of mammalian pre-mRNAs // Nucleic Acids Research. 1990. Y. 18. N. 19. P. 5865—5869. * Gelfand M. S. Statistical analysis and prediction of the exonic structure of human genes // Journal of Molecular Evolution. 1992. Y. 35. N. 2. P. 239—252. * Gelfand M. S. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gelfand–Naimark Theorem
In mathematics, the Gelfand–Naimark theorem states that an arbitrary C*-algebra ''A'' is isometrically *-isomorphic to a C*-subalgebra of bounded operators on a Hilbert space. This result was proven by Israel Gelfand and Mark Naimark in 1943 and was a significant point in the development of the theory of C*-algebras since it established the possibility of considering a C*-algebra as an abstract algebraic entity without reference to particular realizations as an operator algebra. Details The Gelfand–Naimark representation π is the direct sum of representations π''f'' of ''A'' where ''f'' ranges over the set of pure states of A and π''f'' is the irreducible representation associated to ''f'' by the GNS construction. Thus the Gelfand–Naimark representation acts on the Hilbert direct sum of the Hilbert spaces ''H''''f'' by : \pi(x) bigoplus_ H_f= \bigoplus_ \pi_f(x)H_f. π(''x'') is a bounded linear operator since it is the direct sum of a family of operators, each ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gelfand–Naimark–Segal Construction
In functional analysis, a discipline within mathematics, given a C*-algebra ''A'', the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic *-representations of ''A'' and certain linear functionals on ''A'' (called ''states''). The correspondence is shown by an explicit construction of the *-representation from the state. It is named for Israel Gelfand, Mark Naimark, and Irving Segal. States and representations A *-representation of a C*-algebra ''A'' on a Hilbert space ''H'' is a mapping π from ''A'' into the algebra of bounded operators on ''H'' such that * π is a ring homomorphism which carries involution on ''A'' into involution on operators * π is nondegenerate, that is the space of vectors π(''x'') ξ is dense as ''x'' ranges through ''A'' and ξ ranges through ''H''. Note that if ''A'' has an identity, nondegeneracy means exactly π is unit-preserving, i.e. π maps the identity of ''A'' to the identity operator on ''H''. A state on a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gelfand Triple
In mathematics, a rigged Hilbert space (Gelfand triple, nested Hilbert space, equipped Hilbert space) is a construction designed to link the distribution and square-integrable aspects of functional analysis. Such spaces were introduced to study spectral theory in the broad sense. They bring together the 'bound state' (eigenvector) and ' continuous spectrum', in one place. Motivation A function such as the canonical homomorphism of the real line into the complex plane : x \mapsto e^ , is an eigenfunction of the differential operator :-i\frac on the real line R, but isn't square-integrable for the usual Borel measure on R. To properly consider this function as an eigenfunction requires some way of stepping outside the strict confines of the Hilbert space theory. This was supplied by the apparatus of Schwartz distributions, and a ''generalized eigenfunction'' theory was developed in the years after 1950. Functional analysis approach The concept of rigged Hilbert space ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gelfand–Mazur Theorem
In operator theory, the Gelfand–Mazur theorem is a theorem named after Israel Gelfand and Stanisław Mazur which states that a Banach algebra with unit over the complex numbers in which every nonzero element is invertible is isometrically isomorphic to the complex numbers, i. e., the only complex Banach algebra that is a division algebra is the complex numbers C. The theorem follows from the fact that the spectrum of any element of a complex Banach algebra is nonempty: for every element ''a'' of a complex Banach algebra ''A'' there is some complex number ''λ'' such that ''λ''1 − ''a'' is not invertible. This is a consequence of the complex-analyticity of the resolvent function. By assumption, ''λ''1 − ''a'' = 0. So ''a'' = ''λ · ''1. This gives an isomorphism from ''A'' to C. The theorem can be strengthened to the claim that there are (up to isomorphism) exactly three real Banach division algebras: the field of reals R, the fie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gelfond
Gelfand is a surname meaning "elephant" in the Yiddish language. Notable people with the surname include: * Alexander Gelfond (1906–1968), Soviet mathematician * Michael Gelfond, American computer scientist See also * Gelfand * Helfand * Helfant Helfant is a surname meaning "elephant" in the Yiddish language. Notable people with the surname include: * Adam Helfant, sports executive * Edwin Helfant Edwin Helfant (12 April 1926 Margate, New Jersey – 15 February 1978 Ducktown, Atlan ... {{surname Yiddish-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
