Abstract
It is shown that the Gabor frame operator for frames with lattice such thatab=1/N for some integerN≥1 is continuous on the modulation spaces ([9], [20]) whenever the basic functiong is a Schwartz function and (g, a, b) generates a frame forL 2 (R). From this a sufficient condition on the lattice is given which guarantees that one has a Banach frame for the modulation spaces of Feichtinger.
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This work was supported by NSF grant # DMS-8916968 while the author was visiting Yale University.
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Walnut, D.F. Lattice size estimates for Gabor decompositions. Monatshefte für Mathematik 115, 245–256 (1993). https://doi.org/10.1007/BF01300672
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DOI: https://doi.org/10.1007/BF01300672