Fourier coefficients of normalized Cauchy transforms
Complex Variables
2024-10-28 v1 Functional Analysis
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.
Cite
@article{arxiv.2410.19581,
title = {Fourier coefficients of normalized Cauchy transforms},
author = {Adem Limani},
journal= {arXiv preprint arXiv:2410.19581},
year = {2024}
}
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16 pages