Multivariable Interpolation Problems

In this dissertation, we solve multivariable Nevanlinna-Pick type interpolation problems. Particularly, we consider the left tangential interpolation problems on the commutative or noncommutative unit ball. For the commutative setting, we discuss left-tangential operator-argument interpolation problems for Schur-class multipliers on the Drury-Arveson space and for the noncommutative setting, we discuss interpolation problems for Schur-class multipliers on Fock space. We apply the Krein-space geometry approach (also known as the Grassmannian Approach). To implement this approach J-versions of Beurling-Lax representers for shift-invariant subspaces are required. Here we obtain these J-Beurling-Lax theorems by the state-space method for both settings. We see that the Krein-space geometry method is particularly simple in solving the interpolation problems when the Beurling-Lax representer is bounded. The Potapov approach applies equally well whether the representer is bounded or not.

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

2008

Author dc:creator

• Fang, Quanlei

Chair dc:contributor.committeechair

• Ball, Joseph A.

Committee members dc:contributor.committeemember

• Haskell, Peter E.
• Greenberg, William
• Williams, Michael

• Noncommutative Fock space
• Drury-Arveson space
• Nevanlinna-Pick interpolation
• Left-tangential operator-argument problem
• Krein space

Statement dc:rights

• In Copyright

Licence dc:rights.uri

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

Dc Identifier Other

etd-07162008-172556

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/28311