Abstract Multiple orthogonal polynomials with respect to two weights on the step-line are considered. A connection between different dual spectral matrices, one banded (recursion matrix) and Hessenberg, respectively, Gauss–Borel factorization of moment matrix is given. It shown a hidden freedom exhibited by system related multiple polynomials. Pearson equations discussed, Laguerre–Freud conside...

We study weak asymptotic behaviour of the Christoffel--Darboux kernel on main diagonal corresponding to multiple orthogonal polynomials. show that under some hypotheses limit $\tfrac{1}{n} K_n(x,x)\, d\mu$ is same as normalized zero counting measure type II also an extension Nevai's operators our context.

To compute the electrical resistance ( ~ conformal modulus) of a polygonally shaped resistorcut from a sheet of uniform resistivity, it suffices to find a conformal map of the polygon onto arectangle. Constructing such a map requires the solution of a Schwarz-Christoffel parameter prob-lem. First we show by examples that this is practical numerically. Then we consider an inverse 704...