Strong asymptotics of extremal polynomials on the segment in the presence of denumerable set of mass points

Abstract

The strong asymptotics of the monic extremal polynomials with respect to a \(L_{p}(\sigma )\) norm are studied. The measure \(\sigma \) is concentrated on the segment \([-1,1]\) plus a denumerable set of mass points which accumulate at the boundary points of \([-1,1]\) only. Under the assumptions that the mass points satisfy Blaschke's condition and that the absolutely continuous part of \(\sigma \) satisfies Szeg?'s condition.

Keywords

• orthogonal polynomials
• asymptotic behavior