Year: 2025
Type: article
Abstract: We establish estimates for exact upper bounds of deviations of partial Fourier sums $S_{n-1}(f)$ on classes $W^r_{\beta,1}, r>2, \beta\in\mathbb{R},$ of $2\pi$-periodic functions whose $(r,\beta)$-derivatives in the Weyl-Nagy sense belong to the unit ball of the space $L_1$. The specified estimates allow us to write asymptotic equalities for the quantities $\sup\limits_{f\in W^r_{\beta,1}}|f(x)-S_{n-1}(f;x)|$ as $n\rightarrow\infty$, $r\rightarrow\infty$ for arbitrary relations between the parameters $r$ and $n$.
Source: Researches in Mathematics
DOI: 10.15421/242521
Authors: A.S. Serdyuk, I.V. Sokolenko
Institution: Institute of Mathematics
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $20
OpenAlex ID: W4417324143
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