Concerning Asymptotic Behavior for Extremal Polynomials Associated to Nondiagonal Sobolev Norms

Abstract

Let ℙ be the space of polynomials with complex coefficients endowed with a nondiagonal Sobolev norm ∥ · ∥W1,p(Vμ), where the matrix V and the measure μ constitute a p-admissible pair for 1≤p≤∞. In this paper we establish the zero location and asymptotic behavior of extremal polynomials associated to ∥ · ∥W1,p(Vμ), stating hypothesis on the matrix V rather than on the diagonal matrix appearing in its unitary factorization.