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arXiv · 1803.02459

Complex Hyperbolic Geometry and Hilbert Spaces with the Complete Pick Property

Richard Rochberg
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Abstract

Suppose $H$ is a finite dimensional reproducing kernel Hilbert space of functions on $X.$ If $H$ has the complete Pick property then there is an isometric map, $\Phi,$ from $X,$ with the metric induced by $H,$ into complex hyperbolic space, $\mathbb{CH}^{n},$ with its pseudohyperbolic metric. We investigate the relationships between the geometry of $\Phi(X)$ and the function theory of $H$ and its multiplier algebra.

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Richard Rochberg. 2018-03-06. Complex Hyperbolic Geometry and Hilbert Spaces with the Complete Pick Property. https://arxiv.org/abs/1803.02459

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