论加权伯格曼空间 $${{mathcal{B}}_{{2,\mu }}$ 盘中解析函数的最佳近似值

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-09-05 DOI:10.3103/s1066369x24700415

M. R. Langarshoev

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引用次数: 0

摘要

摘要利用代数多项式和伯格曼空间中高阶导数的连续性模数，得到了单位盘中解析函数的最佳近似值之间的尖锐不等式（{{mathcal{B}}_{{2,\mu }}}\) 基于这些不等式，计算了单位盘中解析函数的一些已知类的$n$-宽的精确值。

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On the Best Approximation of Functions Analytic in the Disk in the Weighted Bergman Space $${{\mathcal{B}}_{{2,\mu }}}$$

Abstract

Sharp inequalities between the best approximations of functions analytic in the unit disk are obtained using algebraic polynomials and the moduli of continuity of higher-order derivatives in the Bergman space ${{\mathcal{B}}_{{2,\mu }}}$ Based on these inequalities, the exact values of some known $n$-widths of classes of functions analytic in the unit disk are calculated.

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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.