Spaces of holomorphic almost periodic functions on a strip

Details Spaces of holomorphic almost periodic functions on a strip Spaces of holomorphic almost periodic functions on a strip

2007-01-28

arxiv.org/abs/math/0701812v1

Mat.fiz.,anal.geom., v.11 (2004), No.1, 87-106

Mathematics

Complex Variables

Scientific paper

The notions of almost periodicity in the sense of Weyl and Besicovitch of the order p are extended to holomorphic functions on a strip. We prove that the spaces of holomorphic almost periodic functions in the sense of Weyl for various orders p are the same. These spaces are considerably wider than the space of holomorphic uniformly almost periodic functions and considerably narrower than the spaces of holomorphic almost periodic functions in the sense of Besicovitch. Besides we construct examples showing that the spaces of holomorphic almost periodic functions in the sense of Besicovitch for various orders p are all different.

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