标题： CD 核的弱收敛及其应用 显示英文标题

标题： Weak convergence of CD kernels and applications

摘要： 我们证明了一个关于正交多项式（由测度 $d\mu$定义）的零点计数测度 $d\nu_n$和 $\frac{1}{n} K_n(x,x) d\mu(x)$的弱极限相等的一般性结果。 结合Mate-Nevai和Totik关于$n\lambda_n(x)$的上界，我们证明了关于$d\mu$和$\int_I |\rho_E(x) - \frac{w(x)}{n} K_n(x,x)| dx\to 0$的奇数部分的$\int_I \frac{1}{n} K_n(x,x) d\mu_s\to 0$的一些一般性结果，其中$\rho_E$是平衡测度的密度，$w(x)$是$d\mu$的密度。 显示英文摘要

摘要： We prove a general result on equality of the weak limits of the zero counting measure, $d\nu_n$, of orthogonal polynomials (defined by a measure $d\mu$) and $\frac{1}{n} K_n(x,x) d\mu(x)$. By combining this with Mate--Nevai and Totik upper bounds on $n\lambda_n(x)$, we prove some general results on $\int_I \frac{1}{n} K_n(x,x) d\mu_s\to 0$ for the singular part of $d\mu$ and $\int_I |\rho_E(x) - \frac{w(x)}{n} K_n(x,x)| dx\to 0$, where $\rho_E$ is the density of the equilibrium measure and $w(x)$ the density of $d\mu$.