Abstract:We introduce new quasi-Banach modulation spaces on locally compact abelian 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 Gröchenig 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 … Show more
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.