On norm almost periodic measures

Abstract

In this paper, we study norm almost periodic measures on locally compact Abelian groups. First, we show that the norm almost periodicity of $\mu$ is equivalent to the equi-Bohr almost periodicity of $\mu \ast g$ for all $g$ in a fixed family of functions. Then, we show that, for absolutely continuous measures, norm almost periodicity is equivalent to the Stepanov almost periodicity of the Radon--Nikodym density.

arXiv comment23 pages, added many examples

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Cited by in corpus (3)

• On the Fourier Analysis of Measures with Meyer Set Support
• Model sets with precompact Borel windows
• Fourier Transformable Measures with Meyer set support and their lift to the cut and project scheme