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Pré-Publication, Document De Travail Année : 2016

Intertwining operators associated to a family of differential-reflection operators

Salem Ben Said
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  • PersonId : 977650
Mohamed Sifi
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  • PersonId : 859766

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.
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Dates et versions

hal-01282498 , version 1 (03-03-2016)

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  • HAL Id : hal-01282498 , version 1

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Salem Ben Said, Asma Boussen, Mohamed Sifi. Intertwining operators associated to a family of differential-reflection operators. 2016. ⟨hal-01282498⟩
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