Weak convergence of CD kernels and applications

dc.creatorSimon, Barry
dc.date2007-07-17
dc.date.accessioned2026-07-07T08:18:48Z
dc.date.available2026-07-07T08:18:48Z
dc.descriptionWe 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.identifierhttps://arxiv.org/abs/0707.2578
dc.identifierhttp://arxiv.org/abs/0707.2578
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134559
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.subject33C45; 60B10; 05E35
dc.titleWeak convergence of CD kernels and applications
dc.typetext

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