函数偶数和奇数连续性的均匀有理逼近

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-04-22 DOI:10.1134/s0001434624010206

T. S. Mardvilko

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引用次数: 0

摘要

摘要研究了函数奇续的最佳有理近似的行为。研究表明，如果不对函数的平滑性附加条件，就不可能用原始函数在 \([0,1]\) 上的最佳有理近似值来估计函数在 \([-1,1]\) 上奇数延续的最佳有理近似值。根据奇（偶）续和极值布拉什克积，找到了函数偶（奇）续的最佳有理近似值的尖锐上界。

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Uniform Rational Approximation of Even and Odd Continuations of Functions

Abstract

The behavior of the best rational approximations of an odd continuation of a function is studied. It is shown that without additional conditions on the smoothness of the function, it is impossible to estimate the best rational approximation of the odd continuation of the function on \([-1,1]\) in terms of the best rational approximation of the original function on \([0,1]\). A sharp upper bound is found for the best rational approximations of an even (odd) continuation of a function in terms of an odd (even) continuation and an extremal Blaschke product.

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.