Abstract
We show that a nonvanishing analytic function on a sub-disc of the unit disc can be approximated by (a scalar multiple of) a Blaschke product whose zeros lie on a prescribed circle enclosing the sub-disc. 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.
Citation
David W. Farmer. Pamela Gorkin. "Approximation by polynomials and Blaschke products having all zeros on a circle." Illinois J. Math. 55 (3) 1105 - 1118, Fall 2011. https://doi.org/10.1215/ijm/1369841798
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