The Complete Pick Property and Reproducing Kernel Hilbert Spaces

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Date

2014-01-03

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Volume Title

Publisher

Virginia Tech

Abstract

We present two approaches towards a characterization of the complete Pick property. We first discuss the lurking isometry method used in a paper by J.A. Ball, T.T. Trent, and V. Vinnikov. They show that a nondegenerate, positive kernel has the complete Pick property if 1/k has one positive square. We also look at the one-point extension approach developed by P. Quiggin which leads to a sufficient and necessary condition for a positive kernel to have the complete Pick property. We conclude by connecting the two characterizations of the complete Pick property.

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Keywords

positive kernel, interpolation, multipliers, one-step extension, lurking isometry

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