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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2014

Author dc:creator

• Marx, Gregory

Chair dc:contributor.committeechair

• Ball, Joseph A.

Committee members dc:contributor.committeemember

• Floyd, William J.
• Rossi, John F.

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

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:2095

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/24783