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The Complete Pick Property and Reproducing Kernel Hilbert Spaces

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dc.contributor.authorMarx, Gregoryen
dc.contributor.committeechairBall, Joseph A.en
dc.contributor.committeememberFloyd, William J.en
dc.contributor.committeememberRossi, John F.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-01-04T09:00:12Zen
dc.date.available2014-01-04T09:00:12Zen
dc.date.issued2014-01-03en
dc.description.abstractWe 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.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:2095en
dc.identifier.urihttp://hdl.handle.net/10919/24783en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectpositive kernelen
dc.subjectinterpolationen
dc.subjectmultipliersen
dc.subjectone-step extensionen
dc.subjectlurking isometryen
dc.titleThe Complete Pick Property and Reproducing Kernel Hilbert Spacesen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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