Function theory on the Neil parabola

Abstract

We give a formula for the Carathéodory 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 Carathéodory distance explicitly computed. In addition, we relate this to a mixed Carathéodory-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.

Changed title to match published version

Cited by in corpus (6)

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• Distinguished Varieties Through the Berger--Coburn--Lebow Theorem
• Distinguished varieties and the Nevanlinna-Pick interpolation problem on the symmetrized bidisk
• Polynomial embeddings of unilateral weighted shifts into $2$-variable weighted shifts
• Eigenvalues of Toeplitz Operators on the Annulus and Neil Algebra
• Hyperbolic algebraic and analytic curves