Invariant function spaces as double modules illustrated via Fourier Standard SpacesHans G. Feichtinger (NuHAG, Faculty Mathematics, University Vienna) given at Ghent (Noncommutative Analysis Conf.) (19.08.20) id: 3683 length: min status: accepted type: LINK-Presentation: https://nuhagphp.univie.ac.at/dateien/talks/3683_FeiNonCommut20A.pdf ABSTRACT: The key object of this talk is a certain diagram which can be associated to most of the usual function spaces arising in Fourier analysis over LCA groups. For the sake of convenience we restrict our attention here to the choice G = Rd and the realm of tempered distributions, as a widely known setup. The general results are valid for Banach spaces of ultra-distributions over LCA groups. For each such Banach space we will assign a collection of subspaces, all “with the same norm”, and the diagram will express how they are inter-connected by inclusions (as closed subspaces, from low to high in the diagram). |