Complex Hyperbolic Geometry and Hilbert Spaces with the Complete Pick Property

2018/03/06 by Richard Rochberg, Rochberg, Richard
Mathematics · #46E22 #51M10 #52B11 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1803.02459

openalex publication_date 2018/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, Φ, from X, with the metric induced by H, into complex hyperbolic space, \mathbbCHⁿ, with its pseudohyperbolic metric. We investigate the relationships between the geometry of Φ(X) and the function theory of H and its multiplier algebra.

Citations

• Interpolation and Balls in C^k

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