Some results on Dunkl-coherent Pairs

ABSTRACT

We introduce in this paper the concept of Dunkl-coherent pair of forms (linear functionals) in the symmetric case. We prove that if $\{u,v\}$ is a Dunkl-symmetrically coherent pair of symmetric forms, then at least one of them has to be a symmetric Dunkl-classical form, i.e. Generalized Hermite or Generalized Gegenbauer polynomials.

Keywords:

• Dunkl operator
• orthogonal polynomials
• coherent pairs

AMS CLASSIFICATIONS:

• 33C45
• 42C05

Acknowledgments

The authors thank the referees for their careful revision of the manuscript and for the references brought to their notice. Their helpful comments and suggestions have contributed to improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).