Convolution algebras for Heckman–Opdam polynomials derived from compact Grassmannians

• Heiko Remling ^[2] ; Margit Rösler ^[1]
  1. [1] University of Paderborn

     University of Paderborn

     Kreis Paderborn, Alemania

     
  2. [2] Enggasse 8, Germany
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 197, Nº 1 (September 2015), 2015 (Ejemplar dedicado a: Special Issue Dedicated to Dick Askey on the occasion of his 80th birthday), págs. 30-48
• Idioma: inglés
• DOI: 10.1016/j.jat.2014.07.005
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• Resumen

  • We study convolution algebras associated with Heckman–Opdam polynomials. For root systems of type BCBC we derive three continuous classes of positive convolution algebras (hypergroups) by interpolating the double coset convolution structures of compact Grassmannians U/KU/K with fixed rank over the real, complex or quaternionic numbers. These convolution algebras are linked to explicit positive product formulas for Heckman–Opdam polynomials of type BCBC, which occur for certain discrete multiplicities as the spherical functions of U/KU/K. The results complement those of Rösler (2010) for the noncompact case.