Shift-Modulation invariant spaces in LCA groups

CABRELLI, C.; VICTORIA PATERNOSTRO

STUDIA MATHEMATICA

POLISH ACAD SCIENCES INST MATHEMATICS

Lugar: VARSOVIA; Año: 2012 vol. 211 p. 1 - 19

0039-3223

A (K,Λ) shift-modulation invariant space is a subspace of L2(G) that is invariant by 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 Gˆ, respectively. In this article we provide a characterization of shift-modulation invariant spaces in this general context when K and Λ are uniform lattices. This extends previous results known for L2(Rd). We develop fiberization techniques and suitable range functions adapted to LCA groups needed to provide the desired characterization.