The Strong Asymptotic Analysis of the first kind Orthogonal Trigonometric Polynomial
Huili Han, Hua Liu, Yufeng Wang
TL;DR
This paper performs a detailed asymptotic analysis of first kind orthogonal trigonometric polynomials using Riemann-Hilbert problem techniques for periodic analytic functions.
Contribution
It introduces a novel Riemann-Hilbert approach to analyze the asymptotics of orthogonal trigonometric polynomials of the first kind.
Findings
Derived explicit asymptotic formulas for the polynomials.
Established connections between the polynomials and periodic analytic functions.
Provided a framework for future asymptotic studies of similar orthogonal systems.
Abstract
In this paper we study the asymptotic analysis of the orthogonal trigonometric polynomials by the Riemann-Hilbert problem for the periodic analytic functions.
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Taxonomy
TopicsMathematical functions and polynomials · Algebraic and Geometric Analysis · Matrix Theory and Algorithms