We establish asymptotics for Christoffel functions, and universality limits, associated with multivariate orthogonal polynomials, on the boundary of the unit ball in Rd. Orthogonal Polynomials, Universality Limits, Christoffel functions. 42C05, 42C99, 42B05, 60B20

A software package implementing Schwarz-Christoffel Conformal transformation (or mapping) of doubly connected polygonal regions is fully described in this paper from mathematical, numerical, and practical perspectives. The package solves the so-called accessory parameter problem associated with the mapping function as well as evaluates forward and inverse maps. The robustness of the package is ...

We report on recent progress in the computation of Schwarz–Christoffel maps from bounded or unbounded circular domains to conformally equivalent bounded or unbounded multiply connected polygonal domains. The form of the transformation is given in terms of an integral of an infinite product depending on unknown parameters, namely, the prevertices and the centers and radii of the circles. A syste...

Abstract Contiguous hypergeometric relations for semiclassical discrete orthogonal polynomials are described as Christoffel and Geronimus transformations. Using the Christoffel–Geronimus–Uvarov formulas quasi-determinantal expressions shifted obtained.

Crowding is an intrinsic problem of all numerical conformal mapping techniques. The distance between some of the prevertices of a Schwarz-Christoffel map to an elongated polygon is exponentially small in the aspect ratio of the elongation. We show that a simple change, no domain decomposition or change of canonical domain is needed, to the existing algorithms introduced by Trefethen [L.N. Trefe...

We consider discrete Dirac systems as an approach to the study of corresponding block Toeplitz matrices, which in many ways completes famous via Szegő recurrences and matrix orthogonal polynomials. prove analog Christoffel–Darboux formula derive asymptotic relations for reproducing kernel (using Weyl–Titchmarsh functions systems). These are expressed also terms matrices. case rational (and GBDT...

We consider a new way of factorizing the transition probability matrix discrete-time birth–death chain on integers by means an absorbing and reflecting to state 0 viceversa. First we will reflecting–absorbing factorizations chains integers. give conditions two free parameters such that each factors is stochastic matrix. By inverting order (also known as Darboux transformation) get families “alm...