Sonine Formulas and Intertwining Operators in Dunkl Theory

Dunkl Operators: Theory and Applications

These lecture notes are intended as an introduction to the theory of rational Dunkl operators and the associated special functions, with an emphasis on positivity and asymptotics. We start with an outline of the general concepts: Dunkl operators, the intertwining operator, the Dunkl kernel and the Dunkl transform. We point out the connection with integrable particle systems of Calogero-MoserSut...

Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions⋆

In this paper we prove inversion formulas for the Dunkl intertwining operator Vk and for its dual tVk and we deduce the expression of the representing distributions of the inverse operators V −1 k and V −1 k , and we give some applications.

Orbifold Zhu’s theory associated to intertwining operators

We study intertwining operators among the twisted modules for rational VOAs and show the modular invariance property of the space spanned by the trace functions concerning to some representations of rational orbifold VOAs. Our result generalizes the results obtained in [DLM2] and [M3].

Intertwining Operators and Residues

Dunkl wavelets and applications to inversion of the Dunkl intertwining operator and its dual

These operators are very important inmathematics and physics. They allow the development of generalized wavelets from generalized continuous classical wavelet analysis. Moreover, we have proved in [2] that the generalized two-scale equation associated with the Dunkl operator has a solution and then we can define continuous multiresolution analysis. Dunkl has proved in [1] that there exists a un...