Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product

G. López; Francisco Marcellán; Walter Van Assche

paper

Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product

arXiv:math/9403213

Abstract

We investigate the asymptotic properties of orthogonal polynomials for a class of inner products including the discrete Sobolev inner products $⟨ h, g ⟩ = \int h g d μ + \sum_{j = 1}^{m} \sum_{i = 0}^{N_{j}} M_{j, i} h^{(i)} (c_{j}) g^{(i)} (c_{j})$ , where $μ$ is a certain type of complex measure on the real line, and $c_{j}$ are complex numbers in the complement of $\supp(μ)$. The Sobolev orthogonal polynomials are compared with the orthogonal polynomials corresponding to the measure $μ$ .