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On a generalization of Abelian sequential groups

Saak S. Gabriyelyan (2013)

Fundamenta Mathematicae

Let (G,τ) be a Hausdorff Abelian topological group. It is called an s-group (resp. a bs-group) if there is a set S of sequences in G such that τ is the finest Hausdorff (resp. precompact) group topology on G in which every sequence of S converges to zero. Characterizations of Abelian s- and bs-groups are given. If (G,τ) is a maximally almost periodic (MAP) Abelian s-group, then its Pontryagin dual group ( G , τ ) is a dense -closed subgroup of the compact group ( G d ) , where G d is the group G with the discrete...

On a semigroup of measures with irregular densities

Przemysław Gadziński (2000)

Colloquium Mathematicae

We study the densities of the semigroup generated by the operator - X 2 + | Y | on the 3-dimensional Heisenberg group. We show that the 7th derivatives of the densities have a jump discontinuity. Outside the plane x=0 the densities are C . We give explicit spectral decomposition of images of - X 2 + | Y | in representations.

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