A characterisation of the circle group.
A Characterization of a Class of Locally Compact Abelian Groups via Korovkin Theory.
A characterization of algebraic measures
A characterization of the minimal strongly character invariant Segal algebra
For a locally compact, abelian group , we study the space of functions on belonging locally to the Fourier algebra and with -behavior at infinity. We give an abstract characterization of the family of spaces abelian by its hereditary properties.
A density property of the tori and duality
A generalization of Wienner's criteria for the continuity of a Borel measure
A multiplier theorem for continuous measures
A new proof of the -conjecture for locally compact abelian groups
A note on angular semigroups.
A Perron FrobeniusTheory for Representations of Locally Compact Abelian Groups.
À propos des convoluteurs d'un groupe quotient
An extension of a theorem of F. Forelli.
Another note on Kalton's theorems
Classification of self-dual torsion-free LCA groups
In this paper we seek to describe the structure of self-dual torsion-free LCA groups. We first present a proof of the structure theorem of self-dual torsion-free metric LCA groups. Then we generalize the structure theorem to a larger class of self-dual torsion-free LCA groups. We also give a characterization of torsion-free divisible LCA groups. Consequently, a complete classification of self-dual divisible LCA groups is obtained; and any self-dual torsion-free LCA group can be regarded as an open...
Complemented ideals of group algebras
The existence of a projection onto an ideal I of a commutative group algebra depends on its hull Z(I) ⊆ Ĝ. Existing methods for constructing a projection onto I rely on a decomposition of Z(I) into simpler hulls, which are then reassembled one at a time, resulting in a chain of projections which can be composed to give a projection onto I. These methods are refined and examples are constructed to show that this approach does not work in general. Some answers are also given to previously asked...
Connected LCA groups are sequentially connected
We prove that every connected locally compact Abelian topological group is sequentially connected, i.e., it cannot be the union of two proper disjoint sequentially closed subsets. This fact is then applied to the study of extensions of topological groups. We show, in particular, that if is a connected locally compact Abelian subgroup of a Hausdorff topological group and the quotient space is sequentially connected, then so is .
Corrigendum and addendum to "A generalization of Wiener's criteria for the continuity of a Borel measure"
Countable products of LCA groups: their closed subgroups, quotients and duality properties
Covering locally compact groups by less than many translates of a compact nullset
Gruenhage asked if it was possible to cover the real line by less than continuum many translates of a compact nullset. Under the Continuum Hypothesis the answer is obviously negative. Elekes and Stepr mans gave an affirmative answer by showing that if is the well known compact nullset considered first by Erdős and Kakutani then ℝ can be covered by cof() many translates of . As this set has no analogue in more general groups, it was asked by Elekes and Stepr mans whether such a result holds for...
Dense decompositions of locally compact groups