Positivity of Dunkl's intertwining operator

dc.creatorRösler, Margit
dc.date1997-10-24
dc.date1997-12-11
dc.date.accessioned2026-07-07T05:57:39Z
dc.date.available2026-07-07T05:57:39Z
dc.descriptionFor a finite reflection group on $\b R^N,$ the associated Dunkl operators are parametrized first-order differential-difference operators which generalize the usual partial derivatives. They generate a commutative algebra which is - under weak assumptions - intertwined with the algebra of partial differential operators by a unique linear and homogeneous isomorphism on polynomials. In this paper it is shown that for non-negative parameter values, this intertwining operator is positivity-preserving on polynomials and allows a positive integral representation on certain algebras of analytic functions. This result in particular implies that the generalized exponential kernel of the Dunkl transform is positive-definite.
dc.description18 pages, LaTeX2e; some minor corrections made
dc.identifierhttps://arxiv.org/abs/q-alg/9710029
dc.identifierhttp://arxiv.org/abs/q-alg/9710029
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/88064
dc.subjectQuantum Algebra
dc.subject33C80 (Primary) 44A15, 33C50 (Secondary)
dc.titlePositivity of Dunkl's intertwining operator
dc.typetext

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