Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
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
  • V. Bargmann, Irreducible unitary representations of the Lorentz group, Ann. of Math. (2) 48 (1947), 568-640. MR 9:133a
  • 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
  • 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
  • I. M. Gel'fand and Z. Ja. \v{S}apiro, Representations of the group of rotations in three-dimensional space and their applications, Amer. Math. Soc. Transl. (2) 2 (1956), 207-316. MR 17:875d
  • Harish-Chandra, Spherical functions on a semisimple Lie group. I, Amer. J. Math. 80 (1958), 241–310. MR 94407, DOI
  • 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
  • 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
  • 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
  • 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, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1977. With a foreword by Richard Askey; Encyclopedia of Mathematics and its Applications, Vol. 4. 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
  • 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
  • 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
  • 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