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)


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
Issue number6
Publication statusPublished - Dec 1 2016
Externally publishedYes


  • Differential-reflection operators
  • intertwining operators
  • spectral problem

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Intertwining Operators Associated to a Family of Differential-Reflection Operators'. Together they form a unique fingerprint.

Cite this