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arXiv · 2410.19581

Fourier coefficients of normalized Cauchy transforms

Adem Limani
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Abstract

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.

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Adem Limani. 2024-10-25. Fourier coefficients of normalized Cauchy transforms. https://arxiv.org/abs/2410.19581

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