Sharp estimates for the convergence rate of Fourier series of complex variable functions in L 2(D, p(z))

DOI10.1134/S0965542510060023zbMath1224.43006OpenAlexW2070490039MaRDI QIDQ2995923

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

Publication date: 4 May 2011

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

Full work available at URL: https://doi.org/10.1134/s0965542510060023

zbMATH Keywords

Kolmogorov \(N\)-widthFourier series in terms of orthogonal systemsgeneralized continuity moduleorthogonal systems of functionssharp estimates for the convergence rate

Mathematics Subject Classification ID

Convergence of Fourier series and of inverse transforms (43A50)

Related Items (8)

Approximation by classical orthogonal polynomials with weight in spaces \(L_{2, \gamma }(a,b)\) and widths of some functional classes ⋮ On the best approximation in the mean of functions of a complex variable by Fourier series in the Bergman space ⋮ K-FUNCTIONALS AND EXACT VALUES OF n-WIDTHS IN THE BERGMAN SPACE ⋮ Estimates of the values of \(n\)-widths of classes of analytic functions in the weight spaces \(H_{2,\gamma}(D)\) ⋮ Approximation of functions of a complex variable by Fourier sums in orthogonal systems in \(L_2\) ⋮ Upper bounds for the approximation of certain classes of functions of a complex variable by Fourier series in the space \(L_2\) and \(n\)-widths ⋮ Sharp inequalities between the best root-mean-square approximations of analytic functions in the disk and some smoothness characteristics in the Bergman space ⋮ Mean-square approximation of complex variable functions by Fourier series in the weighted Bergman space

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