The conjugation representation and inner amenability of discrete groups.
The dual group of a dense subgroup
Throughout this abstract, is a topological Abelian group and is the space of continuous homomorphisms from into the circle group in the compact-open topology. A dense subgroup of is said to determine if the (necessarily continuous) surjective isomorphism given by is a homeomorphism, and is determined if each dense subgroup of determines . The principal result in this area, obtained independently by L. Außenhofer and M. J. Chasco, is the following: Every metrizable group is...
The dual space of precompact groups
For any topological group the dual object is defined as the set of equivalence classes of irreducible unitary representations of equipped with the Fell topology. If is compact, is discrete. In an earlier paper we proved that is discrete for every metrizable precompact group, i.e. a dense subgroup of a compact metrizable group. We generalize this result to the case when is an almost metrizable precompact group.
The Fourier Algebra as an Order Ideal of the Fourier-Stieltjes Algebra.
The number of extensions of an invariant mean
The problem of -simple spectrum for ergodic group automorphisms
The structure space of the trigonometric polynomials on a compact group.
The theory of reproducing systems on locally compact abelian groups
A reproducing system is a countable collection of functions such that a general function f can be decomposed as , with some control on the analyzing coefficients . Several such systems have been introduced very successfully in mathematics and its applications. We present a unified viewpoint in the study of reproducing systems on locally compact abelian groups G. This approach gives a novel characterization of the Parseval frame generators for a very general class of reproducing systems on L²(G)....
The Witt group of quadratic characters.
Theorems on lacunary sets, especially p-Sidon sets