Oversampling, quasi-affine frames, and wave packets

Abstract In [E. Hernandez, D. Labate, G. Weiss, J. Geom. Anal. 12 (4) (2002) 615–662], three of the authors obtained a characterization of certain types of reproducing systems. In this work, we apply these results and methods to various affine-like, wave packets and Gabor systems to determine their frame properties. In particular, we study how oversampled systems inherit properties (like the frame bounds) of the original systems. Moreover, our approach allows us to study the phenomenon of oversampling in much greater generality than is found in the literature.

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