Almost periodic currents, chains and divisors in tube domains

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dc.creatorFavorov, S.
dc.creatorRashkovskii, A.
dc.creatorRonkin, L.
dc.date2007-01-29
dc.date.accessioned2026-07-07T07:43:39Z
dc.date.available2026-07-07T07:43:39Z
dc.descriptionA notion of almost periodic current is introduced, as well as a notion of almost periodic holomorphic chain proceeded from that definition. Such a chain can be defined either as a special case of almost periodic currents or as a holomorphic chain whose trace measure is an almost periodic distribution. It is shown that in general situation almost periodicity of the trace of a current does not imply that for the current itself, even if it is closed and positive. The zero set (regarded as a holomorphic chain) of a holomorphic mapping can be represented as a Monge-Ampere type current, and one could expect that the zero set of an almost periodic holomorphic mapping should be almost periodic; however we construct an example of an almost periodic holomorphic mapping whose zero set is not almost periodic. Nevertheless, we prove almost periodicity of the Monge-Ampere currents corresponding to almost periodic holomorphic mappings with certain additional properties. Then we construct functions that play the same role for almost periodic divisors as the so-called Jessen functions for almost periodic holomorphic functions. In terms of Jessen function we give a sufficient condition for realizability of an almost periodic divisor as the divisor of a holomorphic almost periodic function; some necessary condition is obtained, too.
dc.identifierhttps://arxiv.org/abs/math/0701862
dc.identifierhttp://arxiv.org/abs/math/0701862
dc.identifierIsrael. Math. Conf. Proc., v.15 (2001), p.67-88
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122913
dc.subjectComplex Variables
dc.subjectDynamical Systems
dc.subject32H30; 43A60
dc.titleAlmost periodic currents, chains and divisors in tube domains
dc.typetext

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