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Fourier coefficients of normalized Cauchy transforms

Limani, Adem LU (2026) In Journal d'Analyse Mathematique 158(2). p.657-682
Abstract

We consider a certain 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, Katzenelson and Nestoridis on simultaneous approximation. Secondly, we demonstrate the absence of uniform admissible majorants of Fourier coefficients in de Branges–Rovnyak spaces, and deduce complementary results to the classical Ivashev-Musatov Theorem.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal d'Analyse Mathematique
volume
158
issue
2
pages
657 - 682
publisher
Magnes Press
external identifiers
  • scopus:105024690512
ISSN
0021-7670
DOI
10.1007/s11854-025-0414-z
language
English
LU publication?
yes
additional info
Publisher Copyright: © The Author(s) 2025.
id
d2eec3fc-b363-47a3-84d7-40f2e392fed3
date added to LUP
2026-03-02 15:15:56
date last changed
2026-06-10 09:12:22
@article{d2eec3fc-b363-47a3-84d7-40f2e392fed3,
  abstract     = {{<p>We consider a certain 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, Katzenelson and Nestoridis on simultaneous approximation. Secondly, we demonstrate the absence of uniform admissible majorants of Fourier coefficients in de Branges–Rovnyak spaces, and deduce complementary results to the classical Ivashev-Musatov Theorem.</p>}},
  author       = {{Limani, Adem}},
  issn         = {{0021-7670}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{657--682}},
  publisher    = {{Magnes Press}},
  series       = {{Journal d'Analyse Mathematique}},
  title        = {{Fourier coefficients of normalized Cauchy transforms}},
  url          = {{http://dx.doi.org/10.1007/s11854-025-0414-z}},
  doi          = {{10.1007/s11854-025-0414-z}},
  volume       = {{158}},
  year         = {{2026}},
}