用对数-分数-有理函数逼近傅立叶算子的勒贝格常数

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-02-19 DOI:10.3103/s1066369x23110099

I. A. Shakirov

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引用次数: 0

摘要

摘要经典傅里叶算子的 Lebesgue 常数由一个取决于三个参数的对数-分数-有理函数均匀逼近；它们是利用对数和有理逼近的特定性质定义的。对具有不确定（非单调）行为的相应残差项进行了严格研究。所获得的近似结果将已知结果加强了两个数量级以上。

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Approximation of the Lebesgue Constant of the Fourier Operator by a Logarithmic-Fractional-Rational Function

Abstract

The Lebesgue constant of the classical Fourier operator is uniformly approximated by a logarithmic-fractional-rational function depending on three parameters; they are defined using the specific properties of logarithmic and rational approximations. A rigorous study of the corresponding residual term having an indefinite (nonmonotonic) behavior has been carried out. The obtained approximation results strengthen the known results by more than two orders of magnitude.

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来源期刊

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.