On zeros of discrete paraorthogonal polynomials on the unit circle

TL;DR

This paper studies how the zeros of discrete paraorthogonal polynomials on the unit circle change as a real parameter varies, extending previous work on their behavior.

Contribution

It provides a detailed analysis of the zero distribution of discrete paraorthogonal polynomials on the unit circle with respect to a real parameter, building on prior research.

Findings

Zeros exhibit specific patterns as the parameter varies

Zero distribution is closely linked to polynomial properties

Extension of previous zero-behavior results

Abstract

In this note we investigate, as a natural continuation of [K. Castillo, Constr. Approx., 55 (2022) 605-627], the behaviour of the zeros of discrete paraorthogonal polynomials on the unit circle with respect to a real parameter.