Orthogonal trigonometric polynomials from Riemann-Hilbert view
Complex Variables
2021-12-16 v1 Classical Analysis and ODEs
Abstract
In this work, some theorems are established for orthogonal trigonometric polynomials (OTP) including Favard, Baxter, Geronimus, Rakhmanov, Szeg\"o and the strong Szeg\"o theorems which are important in the theory of orthogonal polynomials on the unit circle (OPUC). All these results are based on the mutual representation theorem of OPUC and OTP which deduced by a Riemann-Hilbert problem simultaneously characterizing them. In addition, Szeg\"o recursions, four-term recurrences and some new identities for OPUC and OTP are also obtained by using their Riemann-Hilbert characterizations respectively.
Cite
@article{arxiv.2112.07851,
title = {Orthogonal trigonometric polynomials from Riemann-Hilbert view},
author = {Zhihua Du},
journal= {arXiv preprint arXiv:2112.07851},
year = {2021}
}
Comments
32 pages. arXiv admin note: text overlap with arXiv:0807.3712