Positivity of Dunkl's intertwining operator

Details Positivity of Dunkl's intertwining operator Positivity of Dunkl's intertwining operator

1997-10-24

arxiv.org/abs/q-alg/9710029v2

Mathematics

Quantum Algebra

18 pages, LaTeX2e; some minor corrections made

Scientific paper

For 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.

Affiliated with

Also associated with

No associations

Rating

Positivity of Dunkl's intertwining operator does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Positivity of Dunkl's intertwining operator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Positivity of Dunkl's intertwining operator will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-375168