A note on strong asymptotics of weighted Chebyshev polynomials

JOURNAL OF APPROXIMATION THEORY

卷:181

Article

Kroo, Andras^1,2 

[1] Hungarian Acad Sci, Alfred Renyi Inst Math, H-1051 Budapest, Hungary

[2] Budapest Univ Technol & Econ, Dept Anal, Budapest, Hungary

关键词: Weighted Chebyshev polynomials;    Asymptotics;    Strong unicity constant;   

DOI  :  10.1016/j.jat.2014.01.005

来源: Elsevier

【 摘 要 】

Denote by T-n(., w) the nth degree Chebyshev polynomial with respect to the positive weight w. It is shown in this note that if w is C1+ then T-n(cos phi, w) = K{e(-in phi)pi(2)(e(i phi))} + 0(I) where pi(z) stands for the Szego function corresponding to w. This extends an earlier result proved by Kroo and Peherstorfer who verified this asymptotic relation for C2+alpha, alpha > 0 weights. (c) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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