圆上${L}^2$上复Cauchy变换最佳有理逼近的渐近唯一性
Asymptotic Uniqueness of Best Rational Approximants to Complex Cauchy Transforms in ${L}^2$ of the Circle
摘要：
对任意大的n，证明了函数f在单位圆上L^2意义下n次最佳有理逼近临界点的唯一性，其中f是支撑在（-1，1）中的实区间上的复测度μ的Cauchy变换之和，其Radon-Nikodym导数关于其支撑上的反正弦分布是Dini连续的，非零且具有有界变差的和幅角，以及在μ的支撑上无极点的有理函数。
英文摘要：
For all n large enough, we show uniqueness of a critical point in best rational approximation of degree n, in the L^2-sense on the unit circle, to functions f, where f is a sum of a Cauchy transform of a complex measure μsupported on a real interval included in (-1,1), whose Radon-Nikodym derivative with respect to the arcsine distribution on its support is Dini-continuous, non-vanishing and with and argument of bounded variation, and of a rational function with no poles on the support of μ.
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