Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems
Mathematical Physics
2012-03-01 v2 math.MP
Abstract
Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in the (2+1)-dimensional case, the corresponding system can be extended to 2x2 matrix form. The factorization theorem of the Christoffel kernel for skew orthogonal polynomials in random matrix theory is presented as a by-product of these transformations.
Keywords
Cite
@article{arxiv.1111.7262,
title = {Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems},
author = {Hiroshi Miki and Hiroaki Goda and Satoshi Tsujimoto},
journal= {arXiv preprint arXiv:1111.7262},
year = {2012}
}