The Complete Pick Property and Reproducing Kernel Hilbert Spaces
dc.contributor.author | Marx, Gregory | en |
dc.contributor.committeechair | Ball, Joseph A. | en |
dc.contributor.committeemember | Floyd, William J. | en |
dc.contributor.committeemember | Rossi, John F. | en |
dc.contributor.department | Mathematics | en |
dc.date.accessioned | 2014-01-04T09:00:12Z | en |
dc.date.available | 2014-01-04T09:00:12Z | en |
dc.date.issued | 2014-01-03 | en |
dc.description.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. | en |
dc.description.degree | Master of Science | en |
dc.format.medium | ETD | en |
dc.identifier.other | vt_gsexam:2095 | en |
dc.identifier.uri | http://hdl.handle.net/10919/24783 | en |
dc.publisher | Virginia Tech | en |
dc.rights | In Copyright | en |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
dc.subject | positive kernel | en |
dc.subject | interpolation | en |
dc.subject | multipliers | en |
dc.subject | one-step extension | en |
dc.subject | lurking isometry | en |
dc.title | The Complete Pick Property and Reproducing Kernel Hilbert Spaces | en |
dc.type | Thesis | en |
thesis.degree.discipline | Mathematics | en |
thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
thesis.degree.level | masters | en |
thesis.degree.name | Master of Science | en |
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