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Approximation of the Lebesgue Constant of the Fourier Operator by a Logarithmic Function

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Abstract

The Lebesgue constant Ln of the classical Fourier operator is uniformly approximated by a family of logarithmic functions which depend on two parameters. In this paper, we analyze the case when the corresponding residual term has a nonmonotonous behavior. The obtained data on the approximation of the Lebesgue constants by the mentioned family of functions strengthen the well-known results which correspond to the cases of a strict decrease and increase in the residual term. Various modifications of the logarithmic approximation of Ln are also studied.

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Authors and Affiliations

  1. Naberezhnye Chelny State Pedagogical University, 423806, Naberezhnye Chelny, Russia

    I. A. Shakirov

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  1. I. A. Shakirov
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Correspondence to I. A. Shakirov.

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Brief communication presented by S.R. Nasyrov

Translated by A.V. Shishulin

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Shakirov, I.A. Approximation of the Lebesgue Constant of the Fourier Operator by a Logarithmic Function. Russ Math. 66, 70–76 (2022). https://doi.org/10.3103/S1066369X22050073

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