Weak convergence of CD kernels and applications
| dc.creator | Simon, Barry | |
| dc.date | 2007-07-17 | |
| dc.date.accessioned | 2026-07-07T08:18:48Z | |
| dc.date.available | 2026-07-07T08:18:48Z | |
| dc.description | We prove a general result on equality of the weak limits of the zero counting measure, $dν_n$, of orthogonal polynomials (defined by a measure $dμ$) and $\frac{1}{n} K_n(x,x) dμ(x)$. By combining this with Mate--Nevai and Totik upper bounds on $nλ_n(x)$, we prove some general results on $\int_I \frac{1}{n} K_n(x,x) dμ_s\to 0$ for the singular part of $dμ$ and $\int_I |ρ_E(x) - \frac{w(x)}{n} K_n(x,x)| dx\to 0$, where $ρ_E$ is the density of the equilibrium measure and $w(x)$ the density of $dμ$. | |
| dc.identifier | https://arxiv.org/abs/0707.2578 | |
| dc.identifier | http://arxiv.org/abs/0707.2578 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134559 | |
| dc.subject | Spectral Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | 33C45; 60B10; 05E35 | |
| dc.title | Weak convergence of CD kernels and applications | |
| dc.type | text |