Bulletin des Sciences Mathématiques ( IF 1.241 ) Pub Date : 2020-11-12 , DOI: 10.1016/j.bulsci.2020.102933 Philippe Jaming; Ilona Simon
The aim of this paper is to establish density properties in spaces of the span of powers of functions , in the spirit of the Müntz-Szász Theorem. As density is almost never achieved, we further investigate the density of powers and a modulation of powers . Finally, we establish a Müntz-Szász Theorem for density of translates of powers of cosines . Under some arithmetic restrictions on , we show that density is equivalent to a Müntz-Szász condition on Λ and we conjecture that those arithmetic restrictions are not needed. Some links are also established with the recently introduced concept of Heisenberg Uniqueness Pairs.