High order recurrence relation, Hermite-Pad\'e approximation, and Nikishin systems
Complex Variables
2016-08-06 v1
Abstract
The study of sequences of polynomials satisfying high order recurrence relations is connected with the asymptotic behavior of multiple orthogonal polynomials, the convergence properties of type II Hermite-Pad\'e approximation, and eigenvalue distribution of banded Toeplitz matrices. We present some results for the case of recurrences with constant coefficients which match what is known for the Chebyshev polynomials of the first kind. In particular, under appropriate assumptions, we show that the sequence of polynomials satisfies multiple orthogonality relations with respect to a Nikishin system of measures.
Cite
@article{arxiv.1604.07772,
title = {High order recurrence relation, Hermite-Pad\'e approximation, and Nikishin systems},
author = {D. Barrios Rolanía and J. S. Geronimo and G. López Lagomasino},
journal= {arXiv preprint arXiv:1604.07772},
year = {2016}
}
Comments
27 pages, 3 figures