Differential equations for the radial limits in $\mathbb{Z}_+^2$ of the solutions of a discrete integrable system

A. I. Aptekarev, R. Kozhan


Abstract: A limiting property of the coefficients of the nearest-neighbor recurrence coefficients for the multiple orthogonal polynomials is studying. Namely, assuming existence of the limits along rays of the lattice nearest-neighbor coefficients, we describe the limit in terms of the solution of a system of ordinary differential equations. For Angelesco systems, the result is illustrated numerically.

Keywords: spectral theory difference operators; Jacobi matrices, multiple orthogonal polynomials, nearest-neighbor recurrence relations.

Language: English

DOI: 10.20948/prepr-2018-214-e