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Shift-modulation invariant spaces on LCA groups

Carlos Cabrelli; Victoria Paternostro — 2012

Studia Mathematica

A (K,Λ) shift-modulation invariant space is a subspace of L²(G) that is invariant under translations along elements in K and modulations by elements in Λ. Here G is a locally compact abelian group, and K and Λ are closed subgroups of G and the dual group Ĝ, respectively. We provide a characterization of shift-modulation invariant spaces when K and Λ are uniform lattices. This extends previous results known for $L ² (ℝ^{d})$ . We develop fiberization techniques and suitable range functions adapted to LCA groups...

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