Convolution algebras for Heckman–Opdam polynomials derived from compact Grassmannians

We study convolution algebras associated with Heckman–Opdam polynomials. For root systems of type BC we derive three continuous classes of positive convolution algebras (hypergroups) by interpolating the double coset convolution structures of compact Grassmannians U/K with fixed rank over the real,...

Full description

Saved in:
Bibliographic Details
Published inJournal of approximation theory Vol. 197; pp. 30 - 48
Main Authors Remling, Heiko, Rösler, Margit
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2015
Subjects
Grassmann manifolds
Heckman–Opdam polynomials
Hypergroup convolution
Product formula
53C35
Grassmann manifolds
33C52
Hypergroup convolution
Product formula
43A62
Heckman–Opdam polynomials
33C80
Online AccessGet full text

Cover

More Information
Summary:We study convolution algebras associated with Heckman–Opdam polynomials. For root systems of type BC we derive three continuous classes of positive convolution algebras (hypergroups) by interpolating the double coset convolution structures of compact Grassmannians U/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 BC, which occur for certain discrete multiplicities as the spherical functions of U/K. The results complement those of Rösler (2010) for the noncompact case.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2014.07.005