Sharp two-sided estimate for the sum of a sine series with convex slowly varying sequence of coefficients

DOI10.1007/S10476-020-0047-5zbMath1474.42019OpenAlexW3047427032MaRDI QIDQ2220987

Alexei P. Solodov

Publication date: 25 January 2021

Published in: Analysis Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10476-020-0047-5

zbMATH Keywords

slowly varying functionsine series with monotone coefficientsconvex sequence

Mathematics Subject Classification ID

Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) (42A32)

Related Items (2)

Optimal two-sided estimates on the interval \([\pi/2,\pi\) of the sum of the sine series with convex coefficient sequence] ⋮ Asymptotics of sums of sine series with fractional monotonicity coefficients

Cites Work

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• Smoothness and asymptotic properties of functions with general monotone Fourier coefficients
• Trigonometric series with general monotone coefficients
• Estimates of the sums of sine series with monotone coefficients of certain classes
• Asymptotic behavior of trigonometric series with \(O\)-regularly varying quasimonotone coefficients
• On the behavior of sine series with convex coefficients near the origin
• Asymptotic behavior of trigonometric series with \(O\)-regularly varying quasimonotone coefficients. II
• A sharp lower bound for the sum of a sine series with convex coefficients
• Regularly varying functions

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