On dynamics of asymptotically minimal polynomials

Bayraktar, Turgay and Efe, Melike (2023) On dynamics of asymptotically minimal polynomials. Journal of Approximation Theory, 295 . ISSN 0021-9045 (Print) 1096-0430 (Online)

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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.
Item Type: Article
Uncontrolled Keywords: Brolin measure; Extremal polynomials; Julia set; Klimek topology
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Turgay Bayraktar
Date Deposited: 24 Aug 2023 15:38
Last Modified: 24 Aug 2023 15:38
URI: https://research.sabanciuniv.edu/id/eprint/47660

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