Hermitian symmetric spaces of tube type and multivariate Meixner: Pollaczek polynomials

• Jacques Faraut ^[1] ; Masato Wakayama ^[2]
  1. [1] Université Pierre et Mrie Curie-FRANCE
  2. [2] Institute of Mathematics for Industry Kyushu University-JAPAN
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 120, Nº 1, 2017, págs. 87-114
• Idioma: inglés
• DOI: 10.7146/math.scand.a-25506
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• Resumen

  • Harmonic analysis on Hermitian symmetric spaces of tube type is a natural framework for introducing multivariate Meixner-Pollaczek polynomials. Their main properties are established in this setting: orthogonality, generating and determinantal formulae, difference equations. For proving these properties we use the composition of the following transformations: Cayley transform, Laplace transform, and spherical Fourier transform associated to Hermitian symmetric spaces of tube type. In particular the difference equation for the multivariate Meixner-Pollaczek polynomials is obtained from an Euler type equation on a bounded symmetric domain.