nonsymmetric
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1: 18.38 Mathematical Applications
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Dunkl Type Operators and Nonsymmetric Orthogonal Polynomials
… ►Eigenvalue equations involving Dunkl type operators have as eigenfunctions nonsymmetric analogues of multivariable special functions associated with root systems. This gives also new structures and results in the one-variable case, but the obtained nonsymmetric special functions can now usually be written as a linear combination of two known special functions. … ►The Dunkl type operator is a -difference-reflection operator acting on Laurent polynomials and its eigenfunctions, the nonsymmetric Askey–Wilson polynomials, are linear combinations of the symmetric Laurent polynomial and the ‘anti-symmetric’ Laurent polynomial , where is given in (18.28.1_5). … ►Dunkl type operators and nonsymmetric polynomials have been associated with various other families in the Askey scheme and -Askey scheme, in particular with Wilson polynomials, see Groenevelt (2007), and with Jacobi polynomials, see Koornwinder and Bouzeffour (2011, §7). …2: 15.17 Mathematical Applications
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►First, as spherical functions on noncompact Riemannian symmetric spaces of rank one, but also as associated spherical functions, intertwining functions, matrix elements of SL, and spherical functions on certain nonsymmetric Gelfand pairs.
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3: Bibliography K
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Nonsymmetric Askey-Wilson polynomials as vector-valued polynomials.
Appl. Anal. 90 (3-4), pp. 731–746.
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