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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2410.19581 |
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| _version_ | 1866909365156446208 |
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| author | Limani, Adem |
| author_facet | Limani, Adem |
| contents | We consider a uniqueness problem concerning the Fourier coefficients of normalized Cauchy transforms. These problems inherently involve proving a simultaneous approximation phenomenon and establishing the existence of cyclic inner functions in certain sequence spaces. Our results have several applications in different directions. First, we offer a new non-probabilistic proof of a classic theorem by Kahane and Katzenelson on simultaneous approximation. Secondly, we demonstrate the absence of uniform admissible majorants of Fourier coefficients in de Branges-Rovnyak spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fourier coefficients of normalized Cauchy transforms Limani, Adem Complex Variables Functional Analysis 30J15, 42A16, 30E20 We consider a uniqueness problem concerning the Fourier coefficients of normalized Cauchy transforms. These problems inherently involve proving a simultaneous approximation phenomenon and establishing the existence of cyclic inner functions in certain sequence spaces. Our results have several applications in different directions. First, we offer a new non-probabilistic proof of a classic theorem by Kahane and Katzenelson on simultaneous approximation. Secondly, we demonstrate the absence of uniform admissible majorants of Fourier coefficients in de Branges-Rovnyak spaces. |
| title | Fourier coefficients of normalized Cauchy transforms |
| topic | Complex Variables Functional Analysis 30J15, 42A16, 30E20 |
| url | https://arxiv.org/abs/2410.19581 |