Approximation by polynomials and Blaschke products having all zeros on a circle

David W. Farmer; Pamela Gorkin

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arXiv · 1002.0271

Approximation by polynomials and Blaschke products having all zeros on a circle

David W. Farmer·Pamela Gorkin

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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.

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BibTeX RIS

David W. Farmer, Pamela Gorkin. 2010-02-01. Approximation by polynomials and Blaschke products having all zeros on a circle. https://arxiv.org/abs/1002.0271

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