Frames of exponentials and sub-multitiles in LCA groups

2017/10/09 by Barbieri, Davide, Cabrelli, Carlos, Hernández, Eugenio +3
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1710.03176

Abstract

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⊂ \widehatG with respect to a uniform lattice Γ of \widehatG 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.

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• Multiple lattice tiles and Riesz bases of exponentials