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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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Book Information:

Authors: N. Ja. Vilenkin and A. U. Klimyk
Title: Representation of Lie groups and special functions
Additional book information: Kluwer Acad. Publ., Dordrecht, $804.50 (set). Vol. 1: Simplest Lie groups, special functions and integral transforms, vol. 72, 1991, xxiv + 608 pp., $408.00, ISBN 0-7923-1466-2; Vol. 2: Class I representations, special functions, and integral transforms, vol. 74, 1992, xviii + 607 pp., $397.00, ISBN 0-7923-1492-1; Vol. 3: Classical and quantum groups and special functions, vol. 75, 1992, xx + 634 pp., $397.00, ISBN 0-7923-1493-X,

References [Enhancements On Off] (What's this?)

  • R. A. Askey, T. H. Koornwinder, and W. Schempp (eds.), Special functions: group theoretical aspects and applications, Mathematics and its Applications, D. Reidel Publishing Co., Dordrecht, 1984. MR 774053, DOI 10.1007/978-94-010-9787-1
  • Garrett Birkhoff and Morgan Ward, A characterization of Boolean algebras, Ann. of Math. (2) 40 (1939), 609–610. MR 9, DOI 10.2307/1968945
  • Jean Dieudonné, Special functions and linear representations of Lie groups, CBMS Regional Conference Series in Mathematics, vol. 42, American Mathematical Society, Providence, R.I., 1980. Expository lectures from the CBMS Regional Conference held at East Carolina University, Greenville, North Carolina, March 5–9, 1979. MR 557540
  • 4.
    J. Faraut, Analyse harmonique et fonctions spéciales, in: Deux cours d'analyse harmonique, Birkhaüser, Boston, 1987, pp. 1-151. CMP 19:15
  • George Gasper and Mizan Rahman, Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, vol. 35, Cambridge University Press, Cambridge, 1990. With a foreword by Richard Askey. MR 1052153
  • Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
  • Harish-Chandra, Spherical functions on a semisimple Lie group. I, Amer. J. Math. 80 (1958), 241–310. MR 94407, DOI 10.2307/2372786
  • Gerrit Heckman and Henrik Schlichtkrull, Harmonic analysis and special functions on symmetric spaces, Perspectives in Mathematics, vol. 16, Academic Press, Inc., San Diego, CA, 1994. MR 1313912
  • A. U. Klimyk, Matrichnye èlementy i koèffitsienty Klebsha-Gordana predstavleniĭ grupp, “Naukova Dumka”, Kiev, 1979 (Russian). MR 548464
  • 10.
    E. Koelink, 8 Lectures on quantum groups and q-special functions, Revista Colombiana de Matemáticas 30:2 (1996), 93-180. CMP 97:14
  • Tom H. Koornwinder, Krawtchouk polynomials, a unification of two different group theoretic interpretations, SIAM J. Math. Anal. 13 (1982), no. 6, 1011–1023. MR 674770, DOI 10.1137/0513072
  • Min Ming Tang, Asymptotic stability of some quasilinear parabolic equations in divergence form $L^{\infty }$ results, J. Math. Anal. Appl. 57 (1977), no. 2, 368–381. MR 427796, DOI 10.1016/0022-247X(77)90266-9
  • 13.
    I. G. Macdonald, Affine Hecke algebras and orthogonal polynomials, Séminaire Bourbaki 797 1994-95; Astérisque 237 (1996), 189-207. CMP 97:05
  • Willard Miller Jr., Lie theory and special functions, Mathematics in Science and Engineering, Vol. 43, Academic Press, New York-London, 1968. MR 0264140
  • Willard Miller Jr., Symmetry and separation of variables, Encyclopedia of Mathematics and its Applications, Vol. 4, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1977. With a foreword by Richard Askey. MR 0460751
  • Masatoshi Noumi and Tetsuya Sugitani, Quantum symmetric spaces and related $q$-orthogonal polynomials, Group theoretical methods in physics (Toyonaka, 1994) World Sci. Publ., River Edge, NJ, 1995, pp. 28–40. MR 1413733
  • James D. Talman, Special functions: A group theoretic approach, W. A. Benjamin, Inc., New York-Amsterdam, 1968. Based on lectures by Eugene P. Wigner; With an introduction by Eugene P. Wigner. MR 0239154
  • Audrey Terras, Harmonic analysis on symmetric spaces and applications. I, Springer-Verlag, New York, 1985. MR 791406, DOI 10.1007/978-1-4612-5128-6
  • N. Ja. Vilenkin, Spetsial′nye funktsii i teoriya predstavleniĭ grupp, Izdat. “Nauka”, Moscow, 1965 (Russian). MR 0209523
  • N. Ya. Vilenkin and A. U. Klimyk, Representations of Lie groups, and special functions, Noncommutative harmonic analysis, 2 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1990, pp. 145–268, 270 (Russian). MR 1099425
  • 21.
    N. Ja. Vilenkin and A. U. Klimyk, Representation of Lie Groups and Special Functions. Recent Advances, Mathematics and its Applications 316, Kluwer Academic Publishers, 1994. CMP 96:07
  • Antoni Wawrzyńczyk, Group representations and special functions, Mathematics and its Applications (East European Series), D. Reidel Publishing Co., Dordrecht; PWN—Polish Scientific Publishers, Warsaw, 1984. Examples and problems prepared by Aleksander Strasburger; Translated from the Polish by Bogdan Ziemian. MR 750113, DOI 10.1007/978-94-009-6531-7
  • Eugene P. Wigner, Group theory and its application to the quantum mechanics of atomic spectra, Pure and Applied Physics. Vol. 5, Academic Press, New York-London, 1959. Expanded and improved ed. Translated from the German by J. J. Griffin. MR 0106711

  • Review Information:

    Reviewer: Erik Koelink
    Affiliation: University of Amsterdam
    Reviewer: Tom H. Koornwinder
    Affiliation: University of Amsterdam
    Journal: Bull. Amer. Math. Soc. 35 (1998), 265-270
    Review copyright: © Copyright 1998 American Mathematical Society