对应于解析区域上支撑测度的极值多项式的渐近性质
Asymptotic Properties of Extremal Polynomials Corresponding to Measures Supported on Analytic Regions
摘要：
设G是具有解析边界的单连通有界区域，μ是G的闭包与G外的n个纯点所携带的正测度.给出了L^q（mu）空间中最小范数的首一多项式的范数估计，其中q>0.在范数收敛到0的情况下，我们提供了收敛的收敛速率的估计，推广了以前的几个结果。我们最强大的结果涉及的措施亩，是扰动的措施，是绝对连续的推进的积测度的边界附近的单位磁盘。我们的结果和方法也产生信息的极值多项式的强渐近性和一些信息有关Christoffel函数。
英文摘要：
Let G be a bounded region with simply connected closure and having analytic boundary and let mu be a positive measure carried by the closure of G together with finitely many pure points outside G. We provide estimates on the norms of the monic polynomials of minimal norm in the space L^q(mu) for q>0. In case the norms converge to 0, we provide estimates on the rate of convergence, generalizing several previous results. Our most powerful result concerns measures mu that are perturbations of measures that are absolutely continuous with respect to the push-forward of a product measure near the boundary of the unit disk. Our results and methods also yield information about the strong asymptotics of the extremal polynomials and some information concerning Christoffel functions.
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