Almost periodic currents, chains and divisors in tube domains

Details Almost periodic currents, chains and divisors in tube domains Almost periodic currents, chains and divisors in tube domains

2007-01-29

arxiv.org/abs/math/0701862v1

Israel. Math. Conf. Proc., v.15 (2001), p.67-88

Mathematics

Complex Variables

Scientific paper

A 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.

Affiliated with

Also associated with

No associations

Rating

Almost periodic currents, chains and divisors in tube domains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Almost periodic currents, chains and divisors in tube domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Almost periodic currents, chains and divisors in tube domains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-470427