Sharp estimates for the convergence rate of Fourier series in two variables and their applications

DOI10.1134/S0965542518100020zbMath1405.42007OpenAlexW2899673649MaRDI QIDQ1757724

F. V. Abilova, E. V. Selimkhanov

Publication date: 15 January 2019

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542518100020

zbMATH Keywords

Fourier seriescubature formulageneralized modulus of continuityspherical\(N\)-widthrhombicand hyperbolic sums

Mathematics Subject Classification ID

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

Cites Work

• On exact estimates of the convergence rate of Fourier series for functions of one variable in the space \(L_2[-\pi, \pi\)]
• Sharp estimates for the convergence rate of Fourier-Bessel series
• Sharp estimates for the rate of convergence of double Fourier series in classical orthogonal polynomials
• Sharp estimates for the convergence rate of “hyperbolic” partial sums of double fourier series in orthogonal polynomials
• Sharp estimates for the convergence rate of double Fourier series in terms of orthogonal polynomials in the space L 2((a, b) × (c, d); p(x)q(y))
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