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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2014 Volume 429, Pages 64–81 (Mi znsl6068)

This article is cited 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

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.

UDC: 517.5

Received: 03.09.2014


 English version:
Journal of Mathematical Sciences (New York), 2015, 207:6, 845–856

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