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 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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-3-1,
author = {Saifallah Ghobber and Philippe Jaming},
title = {Uncertainty principles for integral operators},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {197-220},
zbl = {1297.42018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-3-1}
}
Saifallah Ghobber; Philippe Jaming. Uncertainty principles for integral operators. Studia Mathematica, Tome 223 (2014) pp. 197-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-3-1/