Generalized semiclassical orthogonal polynomials on the unit circle: A Riemann-Hilbert perspective

2024/06/11 by Amí lcar Branquinho, Branquinho, Amílcar, Ana Foulquié‐Moreno +3 · 1 citation
Computer Science · Mathematics · #42C05 and 33C45 and 33C47 and 47A56 and 47A75 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical functions and polynomials #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2406.07290

openalex publication_date 2024/06/11 · openalex created_date 2024/06/13 · openalex updated_date 2026/07/28

Abstract

In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain first and second order differential equations for the orthogonal polynomials and associated functions with a weight on the unit circle. We deduce properties for the recurrence relation coefficients from differential properties of the weight. We take the so called generalized modified Jacobi and Bessel weights as a case study.

Cited by

• Three-term Recurrence Relation with Arbitrary Degree Steps for Orthogonal Polynomials

Related

• Differential equations for a class of semiclassical orthogonal polynomials on the unit circle
• Bi-orthogonal Polynomials on the Unit Circle, regular semi-classical Weights and Integrable Systems
• Riemann-Hilbert Methods in the Theory of Orthogonal Polynomials
• Matrix Orthogonal Polynomials: A Riemann--Hilbert approach
• Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle