Approximation of signals in the weighted Zygmund class via Euler-Hausdorff product summability mean of Fourier series. (English) Zbl 1463.42006
Summary: Approximation of functions of Lipschitz and Zygmund classes have been considered by various researchers under different summability means. In the proposed paper, we have studied an estimation of the order of convergence of Fourier series in the weighted Zygmund class \(W(Z_r^{(\omega)})\) by using Euler-Hausdorff product summability mean and accordingly established some (presumably new) results. Moreover, the results obtained here are the generalization of several known results.
MSC:
| 42A20 | Convergence and absolute convergence of Fourier and trigonometric series |
| 40G05 | Cesàro, Euler, Nörlund and Hausdorff methods |
| 41A81 | Weighted approximation |
| 42B08 | Summability in several variables |
Keywords:
degree of approximation; weighted Zygmund class; trigonometric Fourier series; Euler mean; Hausdorff meanReferences:
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