Intertwining operators associated to a family of differential-reflection operators
Résumé
We introduce a family of differential-reflection operators
$\Lambda_{A, \varepsilon}$ acting on smooth functions defined on
$\mathbb R.$ Here $A$ is a Sturm-Liouville function with additional hypotheses and $\varepsilon\in \mathbb R.$ For special pairs $(A,\varepsilon),$ we recover Dunkl's, Heckman's and Cherednik's operators (in one dimension). The spectral problem for the operators $\Lambda_{A, \varepsilon}$ is studied. In particular, we obtain suitable growth estimates for the eigenfunctions of $\Lambda_{A, \varepsilon}$.
As the operators $\Lambda_{A, \varepsilon}$ are mixture of $d/dx$
and reflection operators, we prove the existence of an intertwining
operator $V_{A,\varepsilon}$ between $\Lambda_{A, \varepsilon}$ and the
usual derivative. The positivity of $V_{A,\varepsilon}$ is also established.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...