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arXiv: 1206.1195

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Uncertainty principles for integral operators

Saifallah Ghobber 1, 2, Philippe Jaming 3

(2012-06)

The aim of this paper is to prove new uncertainty principles for an integral operator $\tt$ with a bounded kernel for which there is a Plancherel theorem. The first of these results is an extension of Faris's local uncertainty principle which states that if a nonzero function $f\in L^2(\R^d,\mu)$ is highly localized near a single point then $\tt (f)$ cannot be concentrated in a set of finite measure. The second result extends the Benedicks-Amrein-Berthier uncertainty principle and states that a nonzero function $f\in L^2(\R^d,\mu)$ and its integral transform $\tt (f)$ cannot both have support of finite measure. From these two results we deduce a global uncertainty principle of Heisenberg type for the transformation $\tt$. We apply our results to obtain a new uncertainty principles for the Dunkl and Clifford Fourier transforms.

1:	Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
	Université d'Orléans – CNRS : UMR7349
2:	Analyse harmonique et fonctions spéciales
	Faculté des Sciences de Tunis
3:	Institut de Mathématiques de Bordeaux (IMB)
	CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II

Subject

:

Mathematics/Classical Analysis and ODEs

Keyword(s): Uncertainty principles – annihilating pairs – Dunkl transform – Fourier-Clifford transform – integral operators

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From: Philippe Jaming <>

Submitted on: Wednesday, 6 June 2012 12:14:56

Updated on: Wednesday, 6 June 2012 14:08:43