Article Dans Une Revue Bulletin des Sciences Mathématiques Année : 2018

Density of the span of powers of a function à la Müntz-Szasz

Résumé

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.

Fichier principal
Vignette du fichier
Muntz20160629.pdf (204.96 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence
Loading...

Dates et versions

hal-01338832 , version 1 (29-06-2016)

Licence

Identifiants

Citer

Philippe Jaming, Ilona Simon. Density of the span of powers of a function à la Müntz-Szasz. Bulletin des Sciences Mathématiques, In press. ⟨hal-01338832⟩
241 Consultations
532 Téléchargements

Altmetric

Partager

  • More