Weak limits of zeros of orthogonal polynomials

Let μ be a positive unit Borel measure with infinite support on the interval [−1, 1]. Let P n ( x, μ ) denote the monic orthogonal polynomial of degree n associated with μ , and let v n ( μ ) denote the unit measure with mass 1/ n at each zero of P n ( x, μ ). A carrier is a Borel subset of the support of μ having unit μ -measure, and a measure v is carrier related to μ when it has the same carriers as μ . We demonstrate that for each carrier B of positive capacity there is a measure v , which is carrier related to μ , such that the equilibrium measure of the carrier B is the weak limit of the sequence { v n ( v )} n =1/∞ .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41341/1/365_2005_Article_BF01893436.pd

Cours d'Analyse Infinitésimale

T. II (X, 525 p.)Ante