On the approximation of Weierstrass function via superoscillations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914372879646720 |
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| author | Colombo, Fabrizio Sabadini, Irene Struppa, Daniele C. |
| author_facet | Colombo, Fabrizio Sabadini, Irene Struppa, Daniele C. |
| contents | The Weierstrass function is a classic example of a continuous nowhere differentiable function, defined as a sum of high-frequency complex exponentials. In this paper, we follow a suggestion of M.V. Berry and study the convergence properties of Berry's superoscillating approximation to the truncated Weierstrass function. We provide sharp, explicit error estimates for this approximation and we analyze the subtle convergence properties of the associated double limits. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_05580 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the approximation of Weierstrass function via superoscillations Colombo, Fabrizio Sabadini, Irene Struppa, Daniele C. Classical Analysis and ODEs Complex Variables 35A20 The Weierstrass function is a classic example of a continuous nowhere differentiable function, defined as a sum of high-frequency complex exponentials. In this paper, we follow a suggestion of M.V. Berry and study the convergence properties of Berry's superoscillating approximation to the truncated Weierstrass function. We provide sharp, explicit error estimates for this approximation and we analyze the subtle convergence properties of the associated double limits. |
| title | On the approximation of Weierstrass function via superoscillations |
| topic | Classical Analysis and ODEs Complex Variables 35A20 |
| url | https://arxiv.org/abs/2603.05580 |