The Structure of Translation-Invariant Spaces on Locally Compact Abelian Groups

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The Zak transform and the structure of spaces invariant by the action of an LCA group (2014, methodology): “The proof of it uses the characterization of multiplicative invariant subspaces developed in [5], which is summarized, for the readers convenience, in Subsection 4.”
Reproducing formulas for generalized translation invariant systems on locally compact abelian groups (2014, background): “nly if, NX−1 k=0 g(x−nM−ka)h(x−ka) = 1 M δn,0, ∀x∈{0,1,...,a−1},n∈ {0,1,...,b−1}. This result appears ﬁrst in [42] and has been rediscovered in, e.g., [34]. 4.2 Wavelet and shearlet systems Following [4], we let Epick(G) denote the semigroup of continuous group homomorphisms aof Gonto Gwith compact ”