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Uncertainty principles and characterization of the heat kernel for certain differential-reflection operators
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Salem Ben Saïd
,
Asma Boussen
Published/Copyright:
July 16, 2015
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.
Received: 2014-10-29
Revised: 2015-4-9
Accepted: 2015-4-9
Published Online: 2015-7-16
Published in Print: 2015-10-1
© 2015 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Geometric and harmonic analysis on homogeneous spaces and applications: Hammamet, December 2013
- Some questions related to the Bergman projection in symmetric domains
- Some uncertainty principles for diamond Lie groups
- Uncertainty principles and characterization of the heat kernel for certain differential-reflection operators
- Topology on the unitary dual of completely solvable Lie groups
- Rayleigh theorem, projection of orbital measures and spline functions
Articles in the same Issue
- Frontmatter
- Geometric and harmonic analysis on homogeneous spaces and applications: Hammamet, December 2013
- Some questions related to the Bergman projection in symmetric domains
- Some uncertainty principles for diamond Lie groups
- Uncertainty principles and characterization of the heat kernel for certain differential-reflection operators
- Topology on the unitary dual of completely solvable Lie groups
- Rayleigh theorem, projection of orbital measures and spline functions
