Intertwining Operators Associated to a Family of Differential-Reflection Operators

Salem Ben Said, Asma Boussen, Mohamed Sifi

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We introduce a family of differential-reflection operators Λ A , ε acting on smooth functions defined on R. Here, A is a Sturm–Liouville function with additional hypotheses and - 1 ≤ ε≤ 1. For special pairs (A, ε) , we recover Dunkl’s, Heckman’s and Cherednik’s operators (in one dimension). The spectral problem for the operators Λ A , ε is studied. In particular, we obtain suitable growth estimates for the eigenfunctions of Λ A , ε. As the operators Λ A , ε, are a mixture of d / d x and reflection operators, we prove the existence of an intertwining operator VA , ε between Λ A , ε and the usual derivative. The positivity of VA , ε is also established.

Original languageEnglish
Pages (from-to)4129-4151
Number of pages23
JournalMediterranean Journal of Mathematics
Volume13
Issue number6
DOIs
Publication statusPublished - Dec 1 2016
Externally publishedYes

Keywords

  • Differential-reflection operators
  • intertwining operators
  • spectral problem

ASJC Scopus subject areas

  • Mathematics(all)

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