Frames of exponentials and sub-multitiles in LCA groups

Abstract

In this note we investigate the existence of frames of exponentials for $L^2(Ω)$ in the setting of LCA groups. Our main result shows that sub-multitiling properties of $Ω\subset \widehat{G}$ with respect to a uniform lattice $Γ$ of $\widehat{G}$ guarantee the existence of a frame of exponentials with frequencies in a finite number of translates of the annihilator of $Γ$. 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.