Periodicity of almost periodic zero sets and almost periodic functions

2015/02/28 by Favorov, Sergii Yu.
#30B50 (primary) #42A75 (secondary) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.00175

Abstract

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.

Related

• Sets of values of equivalent almost periodic functions
• Almost periodic discrete sets
• On sums and products of periodic functions
• Definitions of almost periodicity
• On the real projections of zeros of almost periodic functions