Approximation by polynomials and Blaschke products having all zeros on a circle
Complex Variables
2010-02-02 v1 Number Theory
Abstract
We show that a nonvanishing analytic function on a domain in the unit disc can be approximated by (a scalar multiple of) a Blaschke product whose zeros lie on a prescribed circle enclosing the domain. We also give a new proof of the analogous classical result for polynomials. A connection is made to universality results for the Riemann zeta function.
Cite
@article{arxiv.1002.0271,
title = {Approximation by polynomials and Blaschke products having all zeros on a circle},
author = {David W. Farmer and Pamela Gorkin},
journal= {arXiv preprint arXiv:1002.0271},
year = {2010}
}