On dynamics of asymptotically minimal polynomials

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2023-07-29 DOI:10.1016/j.jat.2023.105956

Turgay Bayraktar , Melike Efe

引用次数: 1

Abstract

We study dynamical properties of asymptotically extremal polynomials associated with a non-polar planar compact set $E$ . In particular, we prove that if the zeros of such polynomials are uniformly bounded then their Brolin measures converge weakly to the equilibrium measure of $E$ . In addition, if $E$ is regular and the zeros of such polynomials are sufficiently close to $E$ then we show that the filled Julia sets converge to polynomial convex hull of $E$ in the Klimek topology.

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关于渐近极小多项式的动力学

我们研究了与非极平面紧集E相关的渐近极值多项式的动力学性质。特别地，我们证明了如果这些多项式的零是一致有界的，那么它们的Brolin测度弱收敛于E的平衡测度。此外，如果E是正则的，并且这些多项式的零点足够接近E，则我们证明了在Klimek拓扑中，填充的Julia集收敛于E的多项式凸包。

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

Journal of Approximation Theory 数学-数学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal systems • Interpolation and quadratures • Multivariate approximation • Orthogonal polynomials • Padé approximation • Rational approximation • Spline functions of one and several variables • Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds • Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth) • Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis • Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth) • Gabor (Weyl-Heisenberg) expansions and sampling theory.