Weak Convergence of Cd Kernels and Applications
نویسنده
چکیده
We prove a general result on equality of the weak limits of the zero counting measure, dνn, of orthogonal polynomials (defined by a measure dμ) and 1 n Kn(x, x) dμ(x). By combining this with the asymptotic upper bounds of Máté–Nevai and Totik on nλn(x), we prove some general results on ∫ I 1 n Kn(x, x) dμs → 0 for the singular part of dμ and ∫ I |ρE(x) − w(x) n Kn(x, x)| dx → 0, where ρE is the density of the equilibrium measure and w(x) the density of dμ.
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