论文标题
在$ l _ {\ Mathbb r}^2 $ - 最终的理性近似值，可在几个间隔
On $L_{\mathbb R}^2$-best rational approximants to Markov functions on several intervals
论文作者
论文摘要
令$ f（z）= \ int（z-x）^{ - 1}dμ（x）$，其中$μ$是在$（-1,1）$的几个子中支持的borel量，并具有光滑的radon-nikodym derivative。我们研究了近似值$（f-r_n）（z）$的强大渐近行为，其中$ r_n（z）$是$ l _ {\ mathbb r}^2 $ - 最best otimation to $ f（z）$在单位圆圈内的$ n $ circe上的$ f（z）$。
Let $ f(z)=\int(z-x)^{-1}dμ(x) $, where $ μ$ is a Borel measure supported on several subintervals of $ (-1,1) $ with smooth Radon-Nikodym derivative. We study strong asymptotic behavior of the error of approximation $ (f-r_n)(z) $, where $ r_n(z) $ is the $ L_{\mathbb R}^2$-best rational approximant to $ f(z) $ on the unit circle with $ n $ poles inside the unit disk.
