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).