Saint Petersburg State University, Russia
Date(s) : 20/11/2017 iCal
10 h 00 min - 11 h 00 min
Consider a system of mutually disjoint Jordan curves E:= ∪j=1nEj ⊂ ℂ. We will discuss some problems concerning the ratio asymptotics of the orthogonal polynomials for Szegö measures supported by E. More precisely, let μ be such a measure, and suppose that we perturb the measure μ by adding a finite number of point masses outside of E or by multiplying the weight function by some factor. The following question is addressed: what can be said about the influence of such kind of perturbation on the ratio asymptotics of the corresponding orthogonal polynomials? Note that in case E ⊂ the question about stability of the ratio asymptotics can be reduced to the study of compactness for perturbations of the corresponding Jacobi operator.