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Shift-modulation invariant spaces on LCA groups

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Cabrelli C., Paternostro V.

Studia Mathematica

2012

tom 211

nr 1

1-19

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 $L²(ℝ^{d})$. We develop fiberization techniques and suitable range functions adapted to LCA groups needed to provide the desired characterization.

Ograniczanie wyników

1 Studia Mathematica

1 Cabrelli C.

1 Paternostro V.

1 2012

Wyniki wyszukiwania

Shift-modulation invariant spaces on LCA groups