Boundary interpolation by finite Blaschke products

Vladimir Bolotnikov

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arXiv · 1609.09843

Boundary interpolation by finite Blaschke products

Vladimir Bolotnikov

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Abstract

Given $n$ distinct points $t_1,\ldots,t_n$ on the unit circle $\T$ and equally many target values $\f_1,\ldots,\f_n\in\T$, we describe all Blaschke products $f$ of degree at most $n-1$ such that $f(t_i)=\f_i$ for $i=1,\ldots,n$. We also describe the cases where degree $n-1$ is the minimal possible.

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Vladimir Bolotnikov. 2016-09-30. Boundary interpolation by finite Blaschke products. https://arxiv.org/abs/1609.09843

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