Compactly cogenerated LCA groups

Cotorsion theories cogenerated by א1-free abelian groups

Given an א1-free abelian group G we characterize the class CG of all torsion abelian groups T satisfying Ext(G, T ) = 0 assuming the special continuum hypothesis CH. Moreover, in Gödel’s constructable universe we prove that this characterizes CG for arbitrary torsion-free abelian G. It follows that there exist some ugly א1-free abelian groups.

Landau’s Necessary Density Conditions for Lca Groups

We derive necessary conditions for sampling and interpolation of bandlimited functions on a locally compact abelian group in line with the classical results of H. Landau for bandlimited functions on R. Our conditions are phrased as comparison principles involving a certain canonical lattice.

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

Lattice sub-tilings and frames in LCA groups

Given a lattice Λ in a locally compact abelian group G and a measurable subset Ω with finite and positive measure, then the set of characters associated to the dual lattice form a frame for L2(Ω) if and only if the distinct translates by Λ of Ω have almost empty intersections. Some consequences of this results are the wellknown Fuglede theorem for lattices, as well as a simple characterization ...

Property of Rapid Decay for Extensions of Compactly Generated Groups

In the article we settle down the problem of permanence of property RD under group extensions. We show that if 1 → N → G → Q → 1 is a short exact sequence of compactly generated groups such that Q has property RD, and N has property RD with respect to the restriction of a word-length on G, then G has property RD. We also generalize the result of Ji and Schweitzer stating that locally compact gr...