Uncertainty principles for integral operators

@article{SaifallahGhobber2014,
abstract = {The aim of this paper is to prove new uncertainty principles for integral operators with 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 $f ∈ L²(ℝ^\{d\},μ)$ is highly localized near a single point then (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 $f ∈ L²(ℝ^\{d\},μ)$ and its integral transform (f) cannot both have support of finite measure. From these two results we deduce a global uncertainty principle of Heisenberg type for the transformation . We apply our results to obtain new uncertainty principles for the Dunkl and Clifford Fourier transforms.},
author = {Saifallah Ghobber, Philippe Jaming},
journal = {Studia Mathematica},
keywords = {uncertainty principle; annihilating pairs; integral operators; Fourier-like inversion formula; Plancherel formula; Dunkl transform; Clifford Fourier transform},
language = {eng},
number = {3},
pages = {197-220},
title = {Uncertainty principles for integral operators},
url = {http://eudml.org/doc/285872},
volume = {220},
year = {2014},
}

TY - JOUR
AU - Saifallah Ghobber
AU - Philippe Jaming
TI - Uncertainty principles for integral operators
JO - Studia Mathematica
PY - 2014
VL - 220
IS - 3
SP - 197
EP - 220
AB - The aim of this paper is to prove new uncertainty principles for integral operators with 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 $f ∈ L²(ℝ^{d},μ)$ is highly localized near a single point then (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 $f ∈ L²(ℝ^{d},μ)$ and its integral transform (f) cannot both have support of finite measure. From these two results we deduce a global uncertainty principle of Heisenberg type for the transformation . We apply our results to obtain new uncertainty principles for the Dunkl and Clifford Fourier transforms.
LA - eng
KW - uncertainty principle; annihilating pairs; integral operators; Fourier-like inversion formula; Plancherel formula; Dunkl transform; Clifford Fourier transform
UR - http://eudml.org/doc/285872
ER -