Order estimates of the uniform approximations by Zygmund sums on the classes of convolutions of periodic functions
The Zygmund sums of a function $f\in L_{1}$ are trigonometric polynomials of the form $$Z^{s}_{n-1}(f;t):=\frac{a_{0}}{2}+\sum_{k=1}^{n-1}\Big(1-\big(\frac{k}{n}\big)^{s}\Big) \big(a_{k}(f)\cos kt+b_{k}(f)\sin kt\big), s>0,$$ where $a_{k}(f)$ and $b_{k}(f)$ are the Fourier coefficients of $f$. We...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2021-04-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/4404 |