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

Salem Ben Saïd; Asma Boussen; Mohamed Sifi

doi:10.1515/apam-2015-5010

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

Salem Ben Saïd
, Asma Boussen
, Mohamed Sifi

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We prove various versions of uncertainty principles for a certain Fourier transform F_A. 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 F_A and relate them to the characterization of the heat kernel corresponding to F_A. Heisenberg's and local uncertainty inequalities are also proved.

Original language	English
Pages (from-to)	215-239
Number of pages	25
Journal	Advances in Pure and Applied Mathematics
Volume	6
Issue number	4
DOIs	https://doi.org/10.1515/apam-2015-5010
Publication status	Published - Oct 1 2015
Externally published	Yes

Keywords

Differential-reflection operators
heat kernel
uncertainty principles

ASJC Scopus subject areas

General Mathematics

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10.1515/apam-2015-5010

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abstract = "We prove various versions of uncertainty principles for a certain Fourier transform FA. Here, A is a Ch{\'e}bli 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.",

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AU - Ben Saïd, Salem

AU - Boussen, Asma

AU - Sifi, Mohamed

PY - 2015/10/1

Y1 - 2015/10/1

N2 - 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.

AB - 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.

KW - Differential-reflection operators

KW - heat kernel

KW - uncertainty principles

UR - https://www.scopus.com/pages/publications/84943805825

UR - https://www.scopus.com/pages/publications/84943805825#tab=citedBy

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SP - 215

EP - 239

JO - Advances in Pure and Applied Mathematics

JF - Advances in Pure and Applied Mathematics

IS - 4

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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