Norm asymptotics of orthogonal polynomials for general measures

Abstract

Let μ be a fixed positive unit Borel measure with infinite support in the unit disk. A carrier of μ is any Borel subset B of the support for which μ(B) =1, and another such measure v is carrier-related to μ when it has the same carriers as μ . Let p n (z, v) be the monic orthogonal polynomial of degree n for v . We describe the possible asymptotics for the sequences {(∫| p n ( z,v )| 2 dv )1/2 n } n ≥1 which are associated to the set of measures carrier-related to μ.