We introduce new quasi-Banach modulation spaces on locally compact abelian (LCA) groups which coincide with the classical ones in the Banach setting and prove their main properties. Then we study Gabor frames on quasi-lattices, significantly extending the original theory introduced by Gr\"{o}chenig and Strohmer. These issues are the key tools in showing boundedness results for Kohn-Nirenberg and localization operators on modulation spaces and studying their eigenfunctions' properties. In particular, the results in the Euclidean space are recaptured.

Quasi-Banach modulation spaces and localization operators on locally compact abelian groups / Bastianoni, Federico; Cordero, Elena. - In: BANACH JOURNAL OF MATHEMATICAL ANALYSIS. - ISSN 2662-2033. - 16:4(2022). [10.1007/s43037-022-00205-6]

Quasi-Banach modulation spaces and localization operators on locally compact abelian groups

Bastianoni, Federico;
2022

Abstract

We introduce new quasi-Banach modulation spaces on locally compact abelian (LCA) groups which coincide with the classical ones in the Banach setting and prove their main properties. Then we study Gabor frames on quasi-lattices, significantly extending the original theory introduced by Gr\"{o}chenig and Strohmer. These issues are the key tools in showing boundedness results for Kohn-Nirenberg and localization operators on modulation spaces and studying their eigenfunctions' properties. In particular, the results in the Euclidean space are recaptured.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2973324