Almost periodicity in complex analysis

Periodicity of almost periodic zero sets and almost periodic functions

Whenever all differences between zeros of two holomorphic almost periodic functions in a strip form a discrete set, then both functions are infinite products of periodic functions with commensurable periods. In particular, the result is valid for some classes of Dirichlet series.

狄利克雷级数的概周期性与边值

Almost periodicity and boundary values of Dirichlet series

该研究利用概周期性建立狄利克雷级数哈代空间的Hardy–Stein恒等式与Littlewood–Paley公式对应形式，证明相关极限不可交换，揭示两类边值的性质，并探究其零点集与Blaschke乘积。

Subharmonic Almost Periodic Functions

We prove that almost periodicity in the sense of distributions coincides with almost periodicity with respect to Stepanov's metric for the class of subharmonic functions in a horizontal strip. We also prove that Fourier coefficients of these functions are continuous functions in Im z. Further, if the logarithm of a subharmonic almost periodic function is a subharmonic function, then it is almost periodic.

Spaces of holomorphic almost periodic functions on a strip

The notions of almost periodicity in the sense of Weyl and Besicovitch of the order p are extended to holomorphic functions on a strip. We prove that the spaces of holomorphic almost periodic functions in the sense of Weyl for various orders p are the same. These spaces are considerably wider than the space of holomorphic uniformly almost periodic functions and considerably narrower than the spaces of holomorphic almost periodic functions in the sense of Besicovitch. Besides we construct examples showing that the spaces of holomorphic almost periodic functions in the sense of Besicovitch for v…

超越整函数与其平移共享集合的周期性

Periodicity of Transcendental Entire Functions Sharing Set with their Shifts

本文研究超阶小于1的超越整函数的周期性，证明了当其与平移以权重2共享某集合时函数必具有周期性。

Almost periodic currents, chains and divisors in tube domains

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 coul…