Theorems on Direct and Inverse Approximation by Algebraic Polynomials and Piecewise Polynomials in the Spaces $${{H}^{m}}(a,b)$$ and $$B_{{2,q}}^{s}(a,b)$$

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-05-09 DOI:10.3103/s1066369x24700026

R. Z. Dautov

引用次数: 0

Abstract

The best estimates for the approximation error of functions, defined on a finite interval, by algebraic polynomials and piecewise polynomial functions are obtained in the case when the errors are measured in the norms of Sobolev and Besov spaces. We indicate the weighted Besov spaces, whose functions satisfy Jackson-type and Bernstein-type inequalities and, as a consequence, direct and inverse approximation theorems. In a number of cases, exact constants are indicated in the estimates.

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关于在空间 $${{H}^{m}}(a,b)$$ 和 $$B_{2,q}}^{s}(a,b)$$ 中用代数多项式和分段多项式直接逼近和反逼近的定理

摘要用代数多项式和片断多项式函数定义在有限区间上的函数的近似误差的最佳估计值，是在误差以 Sobolev 和 Besov 空间的规范测量的情况下获得的。我们指出了加权贝索夫空间，其函数满足杰克逊型和伯恩斯坦型不等式，并因此得到了直接和反向逼近定理。在一些情况下，估计值中会指出精确常数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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