Rate of approximation by logarithmic derivatives of polynomials whose zeros lie on a circle

TL;DR

This paper provides an estimate for how quickly logarithmic derivatives of polynomials with zeros on the unit circle can uniformly approximate bounded analytic functions within the unit disk.

Contribution

It introduces a new estimate for the approximation rate of bounded analytic functions by logarithmic derivatives of C-polynomials with zeros on the unit circle.

Findings

Derived an explicit approximation rate estimate

Applicable to bounded analytic functions in the unit disk

Enhances understanding of polynomial approximation methods

Abstract

We obtain an estimate for uniform approximation rate of bounded analytic in the unit disk functions by logarithmic derivatives of $C$-polynomials, i.e., polynomials, all of whose zeros lie on the unit circle $C:|z|=1$.