An uncertainty principle and sampling inequalities in Besov spaces

Philippe Jaming (1) , Eugenia Malinnikova (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Department of Mathematical Sciences

We extend Strichartz's uncertainty principle [18] from the setting of the Sobolov space W 1,2 (R) to more general Besov spaces B 1/p p,1 (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 spaces.

Mots clés: Uncertainty Principle; Besov spaces; Sampling Theory

Domaines: Analyse classique [math.CA]; Analyse fonctionnelle [math.FA]; Variables complexes [math.CV]

Philippe Jaming, Eugenia Malinnikova. An uncertainty principle and sampling inequalities in Besov spaces. Journal of Fourier Analysis and Applications, 2016, 22, pp.768-786. ⟨hal-01135199v2⟩