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

@misc{citeulike:2184971, abstract = {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.}, archivePrefix = {arXiv}, author = {Fabiano, Adelina and Guenot, Jacques and Silipo, James}, citeulike-article-id = {2184971}, citeulike-linkout-0 = {http://arxiv.org/abs/0712.4359}, citeulike-linkout-1 = {http://arxiv.org/pdf/0712.4359}, day = {28}, eprint = {0712.4359}, keywords = {amoeba, tropical}, month = {Dec}, posted-at = {2008-01-01 12:09:01}, priority = {2}, title = {Bochner transforms, perturbations and amoebae of holomorphic almost periodic mappings in tube domains}, url = {http://arxiv.org/abs/0712.4359}, year = {2007} }

TY - ELEC ID - citeulike:2184971 L3 - citeulike-article-id:2184971 N2 - 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. TI - Bochner transforms, perturbations and amoebae of holomorphic almost periodic mappings in tube domains KW - amoeba KW - tropical AU - Fabiano, Adelina AU - Guenot, Jacques AU - Silipo, James PY - 2007/Dec/28/ UR - http://arxiv.org/abs/0712.4359 ER -