Bochner transforms, perturbations and amoebae of holomorphic almost periodic mappings in tube domains

Details Bochner transforms, perturbations and amoebae of holomorphic almost periodic mappings in tube domains Bochner transforms, perturbations and amoebae of holomorphic almost periodic mappings in tube domains

2007-12-28

arxiv.org/abs/0712.4359v1

Complex Var. Elliptic Eq. Vol. 52 No. 8, 2007, 709-739

Mathematics

Complex Variables

Scientific paper

10.1080/17476930701475094

We give an alternative representation of the closure of the Bochner transform of a holomorphic almost periodic mapping in a tube domain. For such mappings we introduce a new notion of amoeba and we show that, for mappings which are regular in the sense of Ronkin, this new notion agrees with Favorov's one. We prove that the amoeba complement of a regular holomorphic almost periodic mapping, defined on Cn and taking its values in Cm+1, is a Henriques m-convex subset of Rn. Finally, we compare some different notions of regularity.

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