An Uncertainty Principle and Sampling Inequalities

Authors: Philippe Jaming Eugenia Malinnikova

Publish Date: 2015/10/23

Volume: 22, Issue: 4, Pages: 768-786

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Abstract

We extend Strichartz’s uncertainty principle Strichartz J Funct Anal 8497–114 1989 from the setting of the Sobolev space W12mathbb R to more general Besov spaces B1/p p1mathbb R The main result gives an estimate from below of the trace of a function from the Besov space on a uniformly distributed discrete subset We also prove the corresponding result in the multivariate case and discuss some applications to irregular approximate sampling in critical Besov spacesThis work was mostly executed while the first author visited the Norwegian University of Science and Technology and the second author visited University of Bordeaux It is our pleasure to thank both Departments for hospitality We are also grateful to an anonymous referee for useful comments and suggestions PhJ kindly acknowledge financial support from the French ANR programs ANR 2011 BS01 007 01 GeMeCod ANR12BS010001 Aventures This study has been carried out with financial support from the French State managed by the French National Research Agency ANR in the frame of the Investments for the future Programme IdEx Bordeaux CPU ANR10IDEX0302 EM was partly supported by Project 213638 of the Research Council of Norway This research was sponsored by the FrenchNorwegian PHC AURORA 2014 PROJECT N 31887TC N 233838 CHARGE

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