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Banach algebras on locally compact groups
In this chapter, we shall consider the classical Banach algebras of harmonic analysis that are associated with a locally compact group G. The class...
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On locally compact groups of small topological entropy
We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the...
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Totally disconnected locally compact groups with just infinite locally normal subgroups
We obtain some global features of totally disconnected locally compact (t.d.l.c.) groups G that are locally isomorphic to a just infinite profinite...
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Locally compact sofic groups
We introduce the notion of soficity for locally compact groups and list a number of open problems.
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Neat locally compact abelian p-groups
Inspired by a result of Kulikov about splitting of pure subgroups in discrete abelian p -groups we classify all locally compact abelian p -groups with...
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Dual Integrable Representations on Locally Compact Groups
Studies of various reproducing function systems emphasized the role of translations and the Fourier periodization function. These influenced the...
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Hardy–Littlewood maximal function on Locally compact Abelian groups
In this paper we investigate a boundedness of the Hardy-Littlewood maximal operator M in the variable Lebesgue spaces in the context locally compact...
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Geometric amenability in totally disconnected locally compact groups
We give a short geometric proof of a result of Soardi and Woess and Salvatori that a quasitransitive graph is amenable if and only if its...
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Riesz Multiresolution Analysis on Locally Compact Abelian Groups: Construction and Exceptions
AbstractIn this article, we construct a Riesz multiresolution analysis (MRA) on locally compact Abelian groups (LCA) starting from a suitably given...
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Generalization of the Heyde Theorem to Some Locally Compact Abelian Groups
According to the well-known Heyde theorem, the Gaussian distribution on the real line is characterized by the symmetry of the conditional...
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Homomorphic images of locally compact groups acting on trees and buildings
We study analogues of Cartan decompositions of Lie groups for totally disconnected locally compact groups. It is shown using these decompositions...
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Point processes, cost, and the growth of rank in locally compact groups
Let G be a locally compact, second countable, unimodular group that is nondiscrete and noncompact. We explore the ergodic theory of invariant point...
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Characterization of locally compact groups by closed totally disconnected subgroups
The purpose of this paper is to provide various characterizations of locally compact groups in terms of their closed totally disconnected subgroups....
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Heyde Theorem for Locally Compact Abelian Groups Containing No Subgroups Topologically Isomorphic to the 2-Dimensional Torus
We prove the following group analogue of the well-known Heyde theorem on a characterization of the Gaussian distribution on the real line. Let X be a...
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Quasi-Banach modulation spaces and localization operators on locally compact abelian groups
We introduce new quasi-Banach modulation spaces on locally compact abelian groups which coincide with the classical ones in the Banach setting and...