Schur-class of finitely connected planar domains: the test-function approach

Simple item page
dc.contributor.authorGuerra Huaman, Moises Danielen
dc.contributor.committeechairBall, Joseph A.en
dc.contributor.committeememberHagedorn, George A.en
dc.contributor.committeememberRenardy, Michael J.en
dc.contributor.committeememberKim, Jong Uhnen
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:10:58Zen
dc.date.adate2011-05-12en
dc.date.available2014-03-14T20:10:58Zen
dc.date.issued2011-04-18en
dc.date.rdate2011-05-12en
dc.date.sdate2011-04-26en
dc.description.abstractWe study the structure of the set of extreme points of the compact convex set of matrix-valued holomorphic functions with positive real part on a finitely-connected planar domain 𝐑 normalized to have value equal to the identity matrix at some prescribed point t₀ ∈ 𝐑. This leads to an integral representation for such functions more general than what would be expected from the result for the scalar-valued case. After Cayley transformation, this leads to a integral Agler decomposition for the matrix Schur class over 𝐑 (holomorphic contractive matrix-valued functions over 𝐑). Application of a general theory of abstract Schur-class generated by a collection of test functions leads to a transfer-function realization for the matrix Schur-class over 𝐑, extending results known up to now only for the scalar case. We also explain how these results provide a new perspective for the dilation theory for Hilbert space operators having 𝐑 as a spectral set.en
dc.description.degreePh. D.en
dc.identifier.otheretd-04262011-111257en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04262011-111257/en
dc.identifier.urihttp://hdl.handle.net/10919/27334en
dc.publisherVirginia Techen
dc.relation.haspartGuerraHuaman_MD_D_2011.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectcompletely positive kernelen
dc.subjectextreme points.en
dc.subjectSchur classen
dc.subjecttest functionsen
dc.titleSchur-class of finitely connected planar domains: the test-function approachen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
GuerraHuaman_MD_D_2011.pdf
Size:
459.91 KB
Format:
Adobe Portable Document Format
Download

Collections

Doctoral Dissertations