{"title":"关于渐近极小多项式的动力学","authors":"Turgay Bayraktar , Melike Efe","doi":"10.1016/j.jat.2023.105956","DOIUrl":null,"url":null,"abstract":"<div><p><span>We study dynamical properties of asymptotically extremal polynomials associated with a non-polar planar compact set </span><span><math><mi>E</mi></math></span><span>. 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 </span><span><math><mi>E</mi></math></span>. In addition, if <span><math><mi>E</mi></math></span> is regular and the zeros of such polynomials are sufficiently close to <span><math><mi>E</mi></math></span><span> then we show that the filled Julia sets<span> converge to polynomial convex hull of </span></span><span><math><mi>E</mi></math></span> in the Klimek topology.</p></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On dynamics of asymptotically minimal polynomials\",\"authors\":\"Turgay Bayraktar , Melike Efe\",\"doi\":\"10.1016/j.jat.2023.105956\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span>We study dynamical properties of asymptotically extremal polynomials associated with a non-polar planar compact set </span><span><math><mi>E</mi></math></span><span>. 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 </span><span><math><mi>E</mi></math></span>. In addition, if <span><math><mi>E</mi></math></span> is regular and the zeros of such polynomials are sufficiently close to <span><math><mi>E</mi></math></span><span> then we show that the filled Julia sets<span> converge to polynomial convex hull of </span></span><span><math><mi>E</mi></math></span> in the Klimek topology.</p></div>\",\"PeriodicalId\":54878,\"journal\":{\"name\":\"Journal of Approximation Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Approximation Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021904523000941\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Approximation Theory","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021904523000941","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We study dynamical properties of asymptotically extremal polynomials associated with a non-polar planar compact set . 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 . In addition, if is regular and the zeros of such polynomials are sufficiently close to then we show that the filled Julia sets converge to polynomial convex hull of in the Klimek topology.
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.