Frames of exponentials and sub-multitiles in LCA groups

DAVIDE BARBIERI, CARLOS CABRELLI, EUGENIO HERNÁNDEZ, PETER LUTHY, URSULA MOLTER, CAROLINA MOSQUERA

COMPTES RENDUS MATHEMATIQUE

ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER

Lugar: Paris; Año: 2017

1631-073X

In this note, we investigate the existence of frames of exponentials for $L^2(Omega)$ in the setting of LCA groups. Our main result shows that sub-multitiling properties of $Omegasubset widehat{G}$ with respect to a uniform lattice $Gamma$ of $widehat{G}$ guarantee the existence of a frame of exponentials with frequencies in a finite number of translates of the annihilator of $Gamma$. We also prove the converse of this result and provide conditions for the existence of these frames. These conditions extend recent results on Riesz bases of exponentials and multitilings to frames.