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St. Petersburg Mathematical Journal

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

 
 

 

On the Sidon inequality for trigonometric polynomials


Author: A. O. Radomskii
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 29 (2017), nomer 4.
Journal: St. Petersburg Math. J. 29 (2018), 643-656
MSC (2010): Primary 42A05
DOI: https://doi.org/10.1090/spmj/1510
Published electronically: June 1, 2018
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

A. O. Radomskii
Affiliation: Steklov Mathematical Institute, Russian Academy of Sciences, Gubkin str. 8, Moscow 119991, Russia
Email: artrad@list.ru

DOI: https://doi.org/10.1090/spmj/1510
Keywords: Trigonometric polynomial, de la Valle\'e-Poussin kernel, Riesz product
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
Article copyright: © Copyright 2018 American Mathematical Society

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