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arXiv · 2603.26123

Harald Bohr's splitting theorem

Viktor Andersson·Ole Fredrik Brevig·Athanasios Kouroupis
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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.

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Viktor Andersson, Ole Fredrik Brevig, Athanasios Kouroupis. 2026-03-27. Harald Bohr's splitting theorem. https://arxiv.org/abs/2603.26123

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