Marx, Gregory2014-01-042014-01-042014-01-03vt_gsexam:2095http://hdl.handle.net/10919/24783We 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.ETDIn Copyrightpositive kernelinterpolationmultipliersone-step extensionlurking isometryThesis