Cyclic subspaces for unitary representations of LCA groups; generalized Zak transform

Abstract

We just published a paper showing that the properties of the shift invariant spaces, $\langle f\rangle$, generated by the translates by $\mathbb{Z}^n$ of an $f$ in $L^2(\mathbb{R}^n)$ correspond to the properties of the spaces $L^2(\mathbb{T}^n,p)$, wh