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Beurling-Figà-Talamanca-Herz algebras

Serap Öztop, Volker Runde, Nico Spronk (2012)

Studia Mathematica

For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras A p ( G , ω ) . For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group Ĝ. For p = 2 and compact G, our approach subsumes an earlier one by H. H. Lee and E. Samei. The key to our approach is not to define Beurling algebras through weights, i.e., possibly unbounded continuous functions, but rather through their inverses, which are bounded continuous functions. We prove that...

On extension of the group operation over the Čech-Stone compactification

Jan Jełowicki (1993)

Colloquium Mathematicae

The convolution of ultrafilters of closed subsets of a normal topological group is considered as a substitute of the extension onto ( β ) 2 of the group operation. We find a subclass of ultrafilters for which this extension is well-defined and give some examples of pathologies. Next, for a given locally compact group and its dense subgroup , we construct subsets of β algebraically isomorphic to . Finally, we check whether the natural mapping from β onto β is a homomorphism with respect to the extension...

Spectral subspaces for the Fourier algebra

K. Parthasarathy, R. Prakash (2007)

Colloquium Mathematicae

In this note we define and explore, à la Godement, spectral subspaces of Banach space representations of the Fourier-Eymard algebra of a (nonabelian) locally compact group.

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