Frames of exponentials and sub-multitiles in LCA groups

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

COMPTES RENDUS MATHEMATIQUE

ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER

Año: 2018 vol. 356 p. 107 - 113

1631-073X

In this note, we investigate the existence of frames of exponentials for L2(Ω) in the setting of LCA groups. Our main result shows that sub-multitiling properties of Ω Ĝ with respect to a uniform lattice Γ of Ĝ 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.