多项式和有理数逼近的几何方法

IF 0.9 2区数学 Q2 MATHEMATICS

International Mathematics Research Notices Pub Date : 2024-04-29 DOI:10.1093/imrn/rnae082

Christopher J Bishop, Kirill Lazebnik

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引用次数: 0

摘要

我们通过证明多项式和有理近似值具有简单的几何结构，强化了魏尔斯特拉斯（Weierstrass）、伦格（Runge）和梅格利安（Mergelyan）的经典近似定理。特别是，当近似一个紧凑集合 $K$ 上的函数 $f$ 时，我们的近似值的临界点可以被认为位于包含 $K$ 的任何给定域中，而所有临界值则位于 $f(K)$ 的多项式凸壳的任何给定邻域中。

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A Geometric Approach to Polynomial and Rational Approximation

We strengthen the classical approximation theorems of Weierstrass, Runge, and Mergelyan by showing the polynomial and rational approximants can be taken to have a simple geometric structure. In particular, when approximating a function $f$ on a compact set $K$, the critical points of our approximants may be taken to lie in any given domain containing $K$, and all the critical values in any given neighborhood of the polynomially convex hull of $f(K)$.

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来源期刊

International Mathematics Research Notices 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

316

审稿时长

1 months

期刊介绍： International Mathematics Research Notices provides very fast publication of research articles of high current interest in all areas of mathematics. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics.