Sharp estimates for the rate of convergence of double Fourier series in classical orthogonal polynomials

DOI10.1134/S0965542515070027zbMath1410.42002OpenAlexW1034528142MaRDI QIDQ500599

M. K. Kerimov, M. V. Abilov, Vladimir A. Abilov

Publication date: 5 October 2015

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

Full work available at URL: https://doi.org/10.1134/s0965542515070027

zbMATH Keywords

generalized modulus of continuitygeneralized shift operator``triangular and ``hyperbolic partial sumsdouble Fourier series in orthogonal polynomialsfunctions having generalized partial derivativessharp estimates for the convergence rate of Fourier series

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Related Items (5)

On exact estimates of the convergence rate of Fourier series for functions of one variable in the space \(L_2[-\pi, \pi\)] ⋮ The projection Galerkin method for solving the time-independent differential diffusion equation in a semi-infinite domain ⋮ On sharp estimates of the convergence of double Fourier-Bessel series ⋮ Unnamed Item ⋮ Sharp estimates for the convergence rate of Fourier series in two variables and their applications

Cites Work

• Mean approximation of functions by algebraic 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))
• Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in L 2((a, b), p(x))
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