A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz+Hankel Determinants

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Authors: Gharakhloo, Roozbeh, Its, Alexander
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211020
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz+Hankel Determinants. Roozbeh Gharakhloo and Alexander Its. SIGMA 16 (2020), 100, 47 pages

In this paper, we will formulate 4×4 Riemann-Hilbert problems for Toeplitz+Hankel determinants and the associated system of orthogonal polynomials, when the Hankel symbol is supported on the unit circle and also when it is supported on an interval [a, b], 0 < a < b < 1. The dist...