JAMING, Philippe; SIMON, Ilona

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JAMING, Philippe
Institut de Mathématiques de Bordeaux [IMB]

SIMON, Ilona
Institute of Mathematics and Informatics, University of Pécs

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Article de revue

Ce document a été publié dans

Bulletin des Sciences Mathématiques. 2018

Elsevier

Date de soutenance

2018

Résumé en anglais

The aim of this paper is to establish density properties in $L^p$ spaces of the span of powers of functions $\{\psi^\lambda\,:\lambda\in\Lambda\}$, $\Lambda\subset\N$ in the spirit of the M\"untz-Sz\'asz Theorem. As density is almost never achieved, we further investigate the density of powers and a modulation of powers $\{\psi^\lambda,\psi^\lambda e^{i\alpha t}\,:\lambda\in\Lambda\}$. Finally, we establish a M\"untz-Sz\'asz Theorem for density of translates of powers of cosines $\{\cos^\lambda(t-\theta_1),\cos^\lambda(t-\theta_2)\,:\lambda\in\Lambda\}$. Under some arithmetic restrictions on $\theta_1-\theta_2$, we show that density is equivalent to a M\"untz-Sz\'asz condition on $\Lambda$ and we conjecture that those arithmetic restrictions are not needed.Some links are also established with the recently introduced concept of Heisenberg Uniqueness Pairs.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194062

Project ANR

Analyse Variationnelle en Tomographies photoacoustique, thermoacoustique et ultrasonore - ANR-12-BS01-0001
Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003

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Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251