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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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On the Sidon inequality for trigonometric polynomials
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by A. O. Radomskii
Translated by: A. Plotkin
St. Petersburg Math. J. 29 (2018), 643-656
DOI: https://doi.org/10.1090/spmj/1510
Published electronically: June 1, 2018
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Abstract:

A lower estimate is established for the uniform norm of a special type trigonometric polynomial in terms of the sum of the $L^{1}$-norms of its summands in the case where the sequence of frequencies splits into finitely many lacunary sequences. The result refines theorems known for lacunary sequences and generalizes a result of Kashin and Temlyakov, which in its turn generalizes the classical Sidon inequality.
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Bibliographic Information
  • A. O. Radomskii
  • Affiliation: Steklov Mathematical Institute, Russian Academy of Sciences, Gubkin str. 8, Moscow 119991, Russia
  • Email: artrad@list.ru
  • Received by editor(s): July 18, 2016
  • Published electronically: June 1, 2018
  • Additional Notes: Supported by the Russian Science Foundation under grant 14-50-00005

    • Dedicated: To Boris Sergeevich Kashin on his 65th birthday
  • © Copyright 2018 American Mathematical Society
  • Journal: St. Petersburg Math. J. 29 (2018), 643-656
  • MSC (2010): Primary 42A05
  • DOI: https://doi.org/10.1090/spmj/1510
  • MathSciNet review: 3708866