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The Complete Pick Property and Reproducing Kernel Hilbert Spaces

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. / Master of Science

Identiferoai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/24783
Date03 January 2014
CreatorsMarx, Gregory
ContributorsMathematics, Ball, Joseph A., Floyd, William J., Rossi, John F.
PublisherVirginia Tech
Source SetsVirginia Tech Theses and Dissertation
Detected LanguageEnglish
TypeThesis
FormatETD, application/pdf
RightsIn Copyright, http://rightsstatements.org/vocab/InC/1.0/

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