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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 ( d ) . We develop fiberization techniques and suitable range functions adapted to LCA groups...

Some results about Beurling algebras with applications to operator theory

Thomas Vils Pedersen (1995)

Studia Mathematica

We prove that certain maximal ideals in Beurling algebras on the unit disc have approximate identities, and show the existence of functions with certain properties in these maximal ideals. We then use these results to prove that if T is a bounded operator on a Banach space X satisfying T n = O ( n β ) as n → ∞ for some β ≥ 0, then n = 1 ( 1 - T ) n x / ( 1 - T ) n - 1 x diverges for every x ∈ X such that ( 1 - T ) [ β ] + 1 x 0 .

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