Weak convergence of CD kernels and applications

Details Weak convergence of CD kernels and applications Weak convergence of CD kernels and applications

2007-07-17

arxiv.org/abs/0707.2578v1

Mathematics

Spectral Theory

Scientific paper

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 $d\mu$.

Affiliated with

Also associated with

No associations

Rating

Weak convergence of CD kernels and applications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Weak convergence of CD kernels and applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weak convergence of CD kernels and applications will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-563243