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 matrixVand the measureμconstitute ap-admissible pair for1≤p≤∞. In this paper we establish the zero location and asymptotic behavior of extremal polynomials associated to∥ · ∥W1,p(Vμ), stating hypothesis on the matrixVrather than on the diagonal matrix appearing in its unitary factorization.