"Quasi-Banach Modulation Spaces and Localization Operators on LCA groups"Bastianoni, FedericoWe define the modulation spaces $M^{p,q}_m$ on a LCA group $\mathcal{G}$ for $0<p,q\leq\infty$. Connections and equivalences with the classical theory for $p,q\geq 1$ by Feichtinger 1983 are exhibited, moreover the Euclidean, discrete and compact cases are fully recovered. We then apply this theory to the study of boundedness properties of pseudodifferential operators. Finally, decay properties for eigenfunctions of localization operators are shown. |
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