Asymptotic Behavior of Sobolev-Type Orthogonal Polynomials on a Rectifiable Jordan Curve or Arc

摘要

Our object of study is the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product langle f, g rangle = ∈t_{E} f(ξ) overline{g(ξ)} ρ(ξ) |d ξ|+ f(Z) A g(Z)^H, where E is a rectifiable Jordan curve or arc in the complex plane