Abstract
Let μ be a compactly supported finite Borel measure in ℂ, and let Πn be the space of holomorphic polynomials of degree at most n furnished with the norm of L 2(μ). We study the logarithmic asymptotic expansions of the norms of the evaluation functionals that relate to polynomials p ∈ Πn their values at a point z ∈ ℂ. The main results demonstrate how the asymptotic behavior depends on regularity of the complement of the support of μ and the Stahl-Totik regularity of the measure. In particular, we study the cases of pointwise and μ-a.e. convergence as n → ∞.
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Original Russian Text Copyright © 2005 Dovgoshei A. A., Abdullaev F., and Kucukaslan M.
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 774–785, July–August, 2005.
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Dovgoshei, A.A., Abdullaev, F. & Kucukaslan, M. The Logarithmic Asymptotic Expansions for the Norms of Evaluation Functionals. Sib Math J 46, 613–622 (2005). https://doi.org/10.1007/s11202-005-0062-6
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DOI: https://doi.org/10.1007/s11202-005-0062-6