Virginia Tech
Schur-class of finitely connected planar domains: the test-function approach
Abstract
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.
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2011
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Guerra Huaman, Moises Daniel
- Chair dc:contributor.committeechair
-
- Ball, Joseph A.
- Committee members dc:contributor.committeemember
-
- Hagedorn, George A.
- Renardy, Michael J.
- Kim, Jong Uhn
Subjects
dc:subject × 4Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-04262011-111257
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/27334