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Approximation by linear methods of classes of $(\psi,\bar\beta)-$differentiable functions

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A.S. Serdyuk, I.V. Sokolenko

Classical Analysis and ODEs · Submitted 6 Mar 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We calculate the least upper bounds for approximations in the metric of the space $L_2$ by linear methods of summation of Fourier series on classes of periodic functions $L^\psi_{\bar\beta,1}$ defined by sequences of multipliers $\psi=\psi(k)$ and shifts of argument $\bar\beta=\beta_k$.

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arXiv ID1303.1300 (version 1)
Pith IDL6MGUXFP, Pith's permanent record of this paper and its review
CitationA.S. Serdyuk, I.V. Sokolenko. "Approximation by linear methods of classes of $(\psi,\bar\beta)-$differentiable functions." arXiv:1303.1300 (2013). https://pith.science/paper/L6MGUXFP
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,737 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.48 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We calculate the least upper bounds for approximations in the metric of the space $L_2$ by linear methods of summation of Fourier series on classes of periodic functions $L^\psi_{\bar\beta,1}$ defined by sequences of multipliers $\psi=\psi(k)$ and shifts of argument $\bar\beta=\beta_k$.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We calculate the least upper bounds for approximations in the metric of the space $L_2$ by linear methods of summation of Fourier series on classes of periodic functions $L^\psi_{\bar\beta,1}$ defined by sequences of multipliers $\psi=\psi(k)$ and shifts of argument $\bar\beta=\beta_k$. contribution 0.70 0.94 0.75 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We calculate the least upper bounds for approximations in the metric of the space $L_2$ by linear methods of summation of Fourier series on classes of periodic functions $L^\psi_{\bar\beta,1}$ defined by sequences of multipliers $\psi=\psi(k)$ and shifts of argument $\bar\beta=\beta_k$.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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