Representation of Lie Groups and Special Functions: Volume 1: Simplest Lie Groups, Special Functions and Integral TransformsSpringer Science & Business Media, 2012 M12 6 - 612 pages This is the first of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. This volume deals with the properties of classical orthogonal polynomials and special functions which are related to representations of groups of matrices of second order and of groups of triangular matrices of third order. This material forms the basis of many results concerning classical special functions such as Bessel, MacDonald, Hankel, Whittaker, hypergeometric, and confluent hypergeometric functions, and different classes of orthogonal polynomials, including those having a discrete variable. Many new results are given. The volume is self-contained, since an introductory section presents basic required material from algebra, topology, functional analysis and group theory. For research mathematicians, physicists and engineers. |
Contents
6 | |
9 | |
Quantum Groups qOrthogonal Polynomials and Basic Hypergeometric Functions | 14 |
Group Representations and Harmonic Analysis | 68 |
Chapter | 92 |
shift operators | 95 |
38 | 155 |
Chapter | 165 |
40 | 330 |
Chapter | 494 |
Wilson polynomials | 559 |
95 | 561 |
595 | |
45 | 597 |
606 | |
608 | |
Other editions - View all
Representation of Lie Groups and Special Functions N. Ja. Vilenkin,A. U. Klimyk No preview available - 1991 |
Representation of Lie Groups and Special Functions: Volume 1: Simplest Lie ... N.Ja. Vilenkin,A.U. Klimyk No preview available - 2012 |
Common terms and phrases
a+i∞o addition theorem analog analytic continuation ati∞o called CGC's Charlier polynomials coefficients complex connected converges corresponding cosh defined denote derive differential equation direct sum equality equivalent Example expansion expression follows from formula Fourier transform function ƒ g₁ given by formula GL(n group SL(2 Hilbert space hypergeometric function implies infinitely differentiable infinitesimal operators integral representation inversion formula irreducible representations Jacobi polynomials K²² kernels l₁ Laguerre polynomials Legendre functions Lie algebra Lie group matrix elements Mellin transform multiplication numbers obtain one-parameter subgroups orthogonal parameters Pmn cosh prove recurrence relations replace representation of G representations Tx Reµ right hand side scalar product Section space of functions subspace substitution symmetry relations T₁ T₂ tanh unitary representations values vector Σπί