Density of Simple Partial Fractions with Poles on a Circle in Weighted Spaces for a Disk and a Segment

IF 0.4 Q4 MATHEMATICS

Vestnik St Petersburg University-Mathematics Pub Date : 2024-04-18 DOI:10.1134/s1063454124010072

M. A. Komarov

引用次数: 0

Abstract

In this paper, we study approximation properties of simple partial fractions (logarithmic derivatives of algebraic polynomials), all of whose poles lie on the unit circle. There are obtained criteria for the density of these fractions in classical integral spaces: in the spaces of functions summable with degree p on the unit segment with ultraspherical weight and (weighted) Bergman spaces, analytic in the unit disk and summable with degree p over the disk area. The well-known criteria of Chui and Newman and Abakumov, Borichev, and Fedorovsky for Bergman spaces with p = 1 and p = 2, respectively, are generalized by the obtained results to the case of an arbitrary exponent p > 0.

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圆盘和线段的加权空间中圆上带极的简单部分分数的密度

摘要本文研究简单偏分数（代数多项式的对数导数）的近似性质，这些分数的极点都位于单位圆上。这些分数在经典积分空间中的密度标准是：在单位段上可求和度数为 p 的函数空间中，具有超球面权重和（加权）伯格曼空间，在单位圆盘中解析，在圆盘区域上可求和度数为 p。Chui 和 Newman 以及 Abakumov、Borichev 和 Fedorovsky 分别针对 p = 1 和 p = 2 的伯格曼空间所提出的著名标准，被所获得的结果推广到了任意指数 p > 0 的情况。

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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来源期刊

Vestnik St Petersburg University-Mathematics MATHEMATICS-

CiteScore

0.70

自引率

50.00%

发文量

期刊介绍： Vestnik St. Petersburg University, Mathematics is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.