Uncertainty principles for integral operators
GHOBBER, Saifallah
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Analyse harmonique et fonctions spéciales
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Analyse harmonique et fonctions spéciales
GHOBBER, Saifallah
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Analyse harmonique et fonctions spéciales
< Reduce
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Analyse harmonique et fonctions spéciales
Language
en
Article de revue
This item was published in
Studia Mathematica. 2014, vol. 220, p. 197--220
Instytut Matematyczny - Polska Akademii Nauk
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Uncertainty principles
annihilating pairs
Dunkl transform
Fourier-Clifford transform
integral operators
Origin
Hal imported