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Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 2, Pages 39–53 (Mi faa3185)  

This article is cited in 1 scientific paper (total in 1 paper)

A quantitative version of the Beurling-Helson theorem

S. V. Konyaginab, I. D. Shkredovca

a Steklov Mathematical Institute of Russian Academy of Sciences
b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow

Abstract: It is proved that any continuous function $\varphi$ on the unit circle such that the sequence $\{e^{in\varphi}\}_{n\in\mathbb{Z}}$ has small Wiener norm $\|e^{in\varphi}\| = o(\log^{1/22}|n|(\log \log |n|)^{-3/11})$, $|n| \to \infty$, is linear. Moreover, lower bounds for the Wiener norms of the characteristic functions of subsets of $\mathbb{Z}_p$ in the case of prime $p$ are obtained.

Keywords: Wiener norm, Beurling-Helson theorem, dissociated sets

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00332
12-01-33080-мол_а_вед
Ministry of Education and Science of the Russian Federation НШ-3082.2014.1
The first author acknowledges the support of RFBR grant no. 14-01-00332 and of the program "Leading Scientific Schools," grant no. 3082.2014.1. The second author acknowledges the support of RFBR grant no. 12-01-33080-mol_a_ved.


DOI: https://doi.org/10.4213/faa3185

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English version:
Functional Analysis and Its Applications, 2015, 49:2, 110–121

Bibliographic databases:

Document Type: Article
UDC: 517.518.45
Received: 14.01.2014

Citation: S. V. Konyagin, I. D. Shkredov, “A quantitative version of the Beurling-Helson theorem”, Funktsional. Anal. i Prilozhen., 49:2 (2015), 39–53; Funct. Anal. Appl., 49:2 (2015), 110–121

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Lebedev V., “Quantitative Aspects of the Beurling-Helson Theorem: Phase Functions of a Special Form”, Studia Math., 247:3 (2019), 273–283  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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