Density of the span of powers of a function à la Müntz-Szasz
Language
en
Article de revue
This item was published in
Bulletin des Sciences Mathématiques. 2018
Elsevier
Date
2018English Abstract
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 ...Read more >
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.Read less <
ANR Project
Analyse Variationnelle en Tomographies photoacoustique, thermoacoustique et ultrasonore - ANR-12-BS01-0001
Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003
Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003
Origin
Hal imported