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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.26123 |
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| _version_ | 1866915894783901696 |
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| author | Andersson, Viktor Brevig, Ole Fredrik Kouroupis, Athanasios |
| author_facet | Andersson, Viktor Brevig, Ole Fredrik Kouroupis, Athanasios |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26123 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Harald Bohr's splitting theorem Andersson, Viktor Brevig, Ole Fredrik Kouroupis, Athanasios Classical Analysis and ODEs 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. |
| title | Harald Bohr's splitting theorem |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2603.26123 |