Title: Frames of exponentials and sub-multitiles in LCA groups,
Abstract: 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 $\Omega \subset \widehat{G}$ 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.