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Displaying 81 – 96 of 96

The conjugation representation and inner amenability of discrete groups.

E. Kaniuth, Annette Markfort (1992)

Journal für die reine und angewandte Mathematik

The dual group of a dense subgroup

William Wistar Comfort, S. U. Raczkowski, F. Javier Trigos-Arrieta (2004)

Czechoslovak Mathematical Journal

Throughout this abstract, $G$ is a topological Abelian group and $\hat{G}$ is the space of continuous homomorphisms from $G$ into the circle group $𝕋$ in the compact-open topology. A dense subgroup $D$ of $G$ is said to determine $G$ if the (necessarily continuous) surjective isomorphism $\hat{G} ↠ \hat{D}$ given by $h \mapsto h | D$ is a homeomorphism, and $G$ is determined if each dense subgroup of $G$ determines $G$ . 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

M. Ferrer, S. Hernández, V. Uspenskij (2013)

Commentationes Mathematicae Universitatis Carolinae

For any topological group $G$ the dual object $\hat{G}$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\hat{G}$ is discrete. In an earlier paper we proved that $\hat{G}$ 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 $G$ is an almost metrizable precompact group.

The Fourier Algebra as an Order Ideal of the Fourier-Stieltjes Algebra.

Jean De Cannière, Ronny Rousseau (1984)

Mathematische Zeitschrift

The number of extensions of an invariant mean

Joseph Max Rosenblatt (1976)

Compositio Mathematica

The problem of $L^{p}$ -simple spectrum for ergodic group automorphisms

A. Iwanik (1991)

Bulletin de la Société Mathématique de France

The structure space of the trigonometric polynomials on a compact group.

Kelly McKennon (1979)

Journal für die reine und angewandte Mathematik

The theory of reproducing systems on locally compact abelian groups

Gitta Kutyniok, Demetrio Labate (2006)

Colloquium Mathematicae

A reproducing system is a countable collection of functions $ϕ_{j} : j \in$ such that a general function f can be decomposed as $f = \sum_{j \in} c_{j} (f) ϕ_{j}$ , with some control on the analyzing coefficients $c_{j} (f)$ . 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)....