Uncertainty principles and characterization of the heat kernel for certain differential-reflection operators

Salem Ben Saïd, Asma Boussen, Mohamed Sifi

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We prove various versions of uncertainty principles for a certain Fourier transform FA. Here, A is a Chébli function (that is, a Sturm-Liouville function with additional hypotheses). We mainly establish an analogue of Beurling's theorem, and its relatives such as theorems of Gelfand-Shilov type, of Morgan type, of Hardy type, and of Cowling-Price type, for FA and relate them to the characterization of the heat kernel corresponding to FA. Heisenberg's and local uncertainty inequalities are also proved.

Original languageEnglish
Pages (from-to)215-239
Number of pages25
JournalAdvances in Pure and Applied Mathematics
Volume6
Issue number4
DOIs
Publication statusPublished - Oct 1 2015
Externally publishedYes

Keywords

  • Differential-reflection operators
  • heat kernel
  • uncertainty principles

ASJC Scopus subject areas

  • Mathematics(all)

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