Abstract
We extend the Gabor analysis in [13] to a broad class of modulation spaces, allowing more general mixed quasi-norm estimates and weights in the definition of the modulation space quasi-norms. For such spaces we deduce invariance and embedding properties, and that the elements admit reconstructible sequence space representations using Gabor frames. We apply these results to show identies between sets of compactly supported elements in modulation spaces and Fourier Lebesgue spaces.
Mathematics Subject Classification (2010). Primary: 46A16, 46Fxx, 42C15, 46A13; Secondary: 46Bxx, 46A40.
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Toft, J. (2015). Gabor Analysis for a Broad Class of Quasi-Banach Modulation Spaces. In: Pilipović, S., Toft, J. (eds) Pseudo-Differential Operators and Generalized Functions. Operator Theory: Advances and Applications(), vol 245. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-14618-8_18
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DOI: https://doi.org/10.1007/978-3-319-14618-8_18
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-14617-1
Online ISBN: 978-3-319-14618-8
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