REPCOP : Repeated-measures planned comparisons and orthogonal polynomials

On Generating Orthogonal Polynomials for Discrete Measures

Orthogonal Polynomials for Area-Type Measures and Image Recovery

Let G be a finite union of disjoint and bounded Jordan domains in the complex plane, let K be a compact subset of G, and consider the set G obtained from G by removing K; i.e., G := G \ K. We refer to G as an archipelago and G as an archipelago with lakes. Denote by {pn(G, z)}n=0 and {pn(G , z)}n=0 the sequences of the Bergman polynomials associated with G and G , respectively, that is, the ort...

Monotonicity of the zeros of orthogonal polynomials through related measures

Relation between two sequences of orthogonal polynomials, where the associated measures are related to each other by a first degree polynomial multiplication (or division), is well known. We use this relation to study the monotonicity properties of the zeros of generalized orthogonal polynomials. As examples, the Jacobi, Laguerre and Charlier polynomials are considered.  2005 Elsevier Inc. All...

Orthogonal Polynomials with Respect to Self-Similar Measures

We study experimentally systems of orthogonal polynomials with respect to self-similar measures. When the support of the measure is a Cantor set, we observe some interesting properties of the polynomials, both on the Cantor set and in the gaps of the Cantor set. We introduce an effective method to visualize the graph of a function on a Cantor set. We suggest a new perspective, based on the theo...

Relative Asymptotics of Orthogonal Polynomials for Perturbed Measures

We survey and present some new results that are related to the behavior of orthogonal polynomials in the plane under small perturbations of the measure of orthogonality. More precisely, we introduce the notion of a polynomially small (PS) perturbation of a measure. Namely, if μ0 ≥ μ1 and {pn(μj , z)}n=0, j = 0, 1, are the associated orthonormal polynomial sequences, then μ0 a PS perturbation of...