Abelianization of Matrix Orthogonal Polynomials
Classical Analysis and ODEs
2021-07-29 v1 Mathematical Physics
Algebraic Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
The main goal of the paper is to connect matrix polynomial biorthogonality on a contour in the plane with a suitable notion of scalar, multi-point Pad\'e approximation on an arbitrary Riemann surface endowed with a rational map to the Riemann sphere. To this end we introduce an appropriate notion of (scalar) multi-point Pad\'e\ approximation on a Riemann surface and corresponding notion of biorthogonality of sections of the semi-canonical bundle (half-differentials). Several examples are offered in illustration of the new notions.
Cite
@article{arxiv.2107.12998,
title = {Abelianization of Matrix Orthogonal Polynomials},
author = {Marco Bertola},
journal= {arXiv preprint arXiv:2107.12998},
year = {2021}
}
Comments
31 pages, 1 figure