Abelianization of Matrix Orthogonal Polynomials

2021/07/27 by Bertola, Marco · 2 citations
#Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2107.12998

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 Padé 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 Padé 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.

Cited by

• The generalized Chebotarev problem in higher genus
• Recurrence relations and the Christoffel-Darboux formula for elliptic orthogonal polynomials

Related

• Padé approximants on Riemann surfaces and KP tau functions
• Nonlinear steepest descent approach to orthogonality on elliptic curves
• Matrix orthogonality in the plane versus scalar orthogonality in a Riemann surface
• Riemann-Hilbert Characterisation of Rational Functions with a General Distribution of Poles on the Extended Real Line Orthogonal with Respect to Varying Exponential Weights: Multi-Point Padé Approximants and Asymptotics
• The 2-matrix model, biorthogonal polynomials, Riemann-Hilbert problem, and algebraic geometry