Harald Bohr's splitting theorem
Classical Analysis and ODEs
2026-03-30 v1
Abstract
We present a new elementary proof of a theorem due to Harald Bohr, which states that an unbounded, analytic, and almost periodic function in a half-plane can be written as the sum of two analytic functions: the first is unbounded and periodic, while the second is bounded and almost periodic. The proof is based on a well-known arithmetical property of translation numbers of almost periodic functions.
Keywords
Cite
@article{arxiv.2603.26123,
title = {Harald Bohr's splitting theorem},
author = {Viktor Andersson and Ole Fredrik Brevig and Athanasios Kouroupis},
journal= {arXiv preprint arXiv:2603.26123},
year = {2026}
}