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Function theory on the Neil parabola

Greg Knese
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Abstract

We give a formula for the Carath\'eodory distance on the Neil parabola, the variety ${z^2=w^3}$ restricted to the bidisk; thus making it the first variety with a singularity to have its Carath\'eodory distance explicitly computed. In addition, we relate this to a mixed Carath\'eodory-Pick interpolation problem for which known interpolation theorems do not apply. Finally, we prove a bounded holomorphic function extension result from the Neil parabola to the bidisk.

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Greg Knese. 2005-12-20. Function theory on the Neil parabola. https://doi.org/10.1307/mmj/1177681989

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