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arXiv · 1710.02955

The 3-point spectral Pick interpolation problem and an application to holomorphic correspondences

Vikramjeet Singh Chandel
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Abstract

We provide a necessary condition for the existence of a 3-point holomorphic interpolant $F:\mathbb{D}\longrightarrowΩ_n$, $n\geq 2$. Our condition is inequivalent to the necessary conditions hitherto known for this problem. The condition generically involves a single inequality and is reminiscent of the Schwarz lemma. We combine some of the ideas and techniques used in our result on the $\mathcal{O}(\mathbb{D},Ω_n)$-interpolation problem to establish a Schwarz lemma -- which may be of independent interest -- for holomorphic correspondences from $\mathbb{D}$ to a general planar domain $Ω\Subset \mathbb{C}$.

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Vikramjeet Singh Chandel. 2017-10-09. The 3-point spectral Pick interpolation problem and an application to holomorphic correspondences. https://doi.org/10.1007/s12220-018-00123-w

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