Differential equations and recursion relations for Laguerre functions on symmetric cones

DOI10.1090/S0002-9947-07-04062-7zbMath1126.33002MaRDI QIDQ3431212

Hongming Ding

Publication date: 5 April 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

recurrence relationLaguerre polynomialspherical polynomialJordan algebrasymmetric coneLaguerre function

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15)

Cites Work

• Generalized binomial coefficients and Macdonald polynomials
• Ramanujan's master theorem for symmetric cones
• Laplace and Segal--Bargmann transforms on Hermitian symmetric spaces and orthogonal poly\-nomials.
• Laguerre polynomials, restriction principle, and holomorphic representations of SL\((2\mathbb R)\)
• Generalized principal series representations and tube domains
• Differential recursion relations for Laguerre functions on Hermitian matrices
• Some Recurrence Formulas for Spherical Polynomials on Tube Domains
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