Favard, Baxter, Geronimus, Rakhmanov, Szeg\"o and the strong Szeg\"o theorems for orthogonal trigonometric polynomials
Zhihua Du
TL;DR
This paper extends classical theorems from orthogonal polynomials on the unit circle to orthogonal trigonometric polynomials, using a mutual representation theorem as a key tool.
Contribution
It introduces analogs of major theorems for OTP, bridging the theory of OPUC and OTP with a new representation approach.
Findings
Established Favard, Baxter, Geronimus, Rakhmanov, Szeg"o, and strong Szeg"o theorems for OTP
Developed a mutual representation theorem linking OPUC and OTP
Provided new insights into the structure of orthogonal trigonometric polynomials
Abstract
In this paper, we obtain some analogs of Favard, Baxter, Geronimus, Rakhmanov, Szeg\"o and the strong Szeg\"o theorems appeared in the theory of orthogonal polynomials on the unit circle (OPUC) for orthogonal trigonometric polynomials (OTP). The key tool is the mutual representation theorem for OPUC and OTP.
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Taxonomy
TopicsMathematical functions and polynomials · Matrix Theory and Algorithms · Iterative Methods for Nonlinear Equations