No abstract

We give an intrinsic estimate of the number of connected components of the complementary set to the amoeba of an exponential sum with real spectrum improving the result of Forsberg, Passare and Tsikh in the polynomial case and that of Ronkin in the exponential one.

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 C n and taking its values in C m+1 , is a Henriques m-convex subset of R n . Finally, we compare some different notions of regularity.

The present paper provides a detailed and almost self-contained introduction to Kazarnovskiǐ mixed pseudovolume. MSC: Primary 52A39.