Lp-Fourier analysis for certain differential-reflection operators

Salem Ben Said, Asma Boussen, Mohamed Sifi

Research output: Contribution to journalArticlepeer-review


In a previous paper we introduced a family of differential-reflection operators ΛA , ϵ acting on smooth functions defined on R, where the spectral problem for the operators ΛA,ϵ has been studied. Here A is a Sturm-Liouville function with additional hypotheses and-1 ≤ ϵ ≤ 1. Via the eigenfunctions of ΛA,ϵ, we introduce in this paper a generalized Fourier transform fA,ϵ. An Lp-harmonic analysis for fA,ϵ is developed when 0 < p ≤ 2/1 + 1-ϵ2. In particular, an Lp-Schwartz space isomorphism theorem for fA,ϵ is proved.

Original languageEnglish
Pages (from-to)43-63
Number of pages21
JournalAdvances in Pure and Applied Mathematics
Issue number1
Publication statusPublished - Jan 1 2017
Externally publishedYes


  • Differential-reflection operators
  • L-harmonic analysis
  • generalized Fourier transform

ASJC Scopus subject areas

  • General Mathematics


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