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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 429, Pages 64–81 (Mi znsl6068)  
This article is cited in 1 scientific paper (total in 1 paper)

Some inequalities for trigonometric polynomials and Fourier coefficients

V. V. Zhuka, G. Yu. Puerovbc

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg National Research University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia
c "Okeanpribor", St. Petersburg, Russia
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Abstract: The Bernstein inequalities for trigonometric polynomials are generalized. For the sums of Fourier coefficients, upper bounds with certain constants are obtained with respect to values that characterize the structural properties of functions.
Key words and phrases: trigonometric polynomials, Bernstein's inequality for derivatives, exact constants, moduli of continuity, Fourier coefficients.
Received: 03.09.2014
English version:
Journal of Mathematical Sciences (New York), 2015, Volume 207, Issue 6, Pages 845–856
DOI: https://doi.org/10.1007/s10958-015-2409-2
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: V. V. Zhuk, G. Yu. Puerov, “Some inequalities for trigonometric polynomials and Fourier coefficients”, Analytical theory of numbers and theory of functions. Part 29, Zap. Nauchn. Sem. POMI, 429, POMI, St. Petersburg, 2014, 64–81; J. Math. Sci. (N. Y.), 207:6 (2015), 845–856
Citation in format AMSBIB
\Bibitem{ZhuPue14}
\by V.~V.~Zhuk, G.~Yu.~Puerov
\paper Some inequalities for trigonometric polynomials and Fourier coefficients
\inbook Analytical theory of numbers and theory of functions. Part~29
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 429
\pages 64--81
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6068}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 207
\issue 6
\pages 845--856
\crossref{https://doi.org/10.1007/s10958-015-2409-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84949626979}
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  • https://www.mathnet.ru/eng/znsl/v429/p64
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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