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We prove that in Polish, abelian, non-locally-compact groups the family of Haar null sets of Christensen does not fulfil the countable chain condition, that is, there exists an uncountable family of pairwise disjoint universally measurable sets which are not Haar null. (Dougherty, answering an old question of Christensen, showed earlier that this was the case for some Polish, abelian, non-locally-compact groups.) Thus we obtain the following characterization of locally compact, abelian groups: Let...
We consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in or . We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally compact, abelian groups are considered. We define generalized Marcinkiewicz spaces based upon arbitrary measure spaces...
We study the notion of left -biflatness for Segal algebras and semigroup algebras. We show that the Segal algebra is left -biflat if and only if is amenable. Also we characterize left -biflatness of semigroup algebra in terms of biflatness, when is a Clifford semigroup.
We investigate positive definiteness of the Brownian kernel K(x,y) = 1/2(d(x,x₀) + d(y,x₀) - d(x,y)) on a compact group G and in particular for G = SO(n).
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