【摘 要】
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In this talk,we analyze the asymptic behaviour of the sequence{pn}of orthogonal polynomials on the unit disk D with respect to a weight ω≥ 0,namely:ZD ∫DPˉk
【机 构】
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ProjetAPICS,INRIASophia-Antipolis,France
【出 处】
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International Conference on Orthogonal Polynomials,Integrabl
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In this talk,we analyze the asymptic behaviour of the sequence{pn}of orthogonal polynomials on the unit disk D with respect to a weight ω≥ 0,namely:ZD ∫DPˉkωdm = δn,kwhere the leading coefficient is normalized to be positive:Pn(z)=κnzn + a(n)n-1zn-1 +...+ a(n)0,kn ＞ 0Letting ωrindicate the restiction of ω to the circle of radius r ＜ 1,we assume that for some p ＞ 1ω1 := lim r→1-ωr exisits in Lp(T)and also that supr0＜r＜1 ∫T log-ωr log+ log-ωr ＜ c ＜ +∞Under these conditions,we provide exterior asymptotics forPn.In particular,it holds for the dominant coefficient that limn→+∞ κn/√n + 1 =(π(G)ω1)-1/2where(G)ω∞ is the geometric mean of ω1.This generalizes results of [1],[3],and also of [2](for the special case of the disk)in that we do not assume that ω has a product structure.
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