| Type of Document |
Dissertation |
| Author |
Fang, Quanlei
|
| Author's Email Address |
qlfang@vt.edu |
| URN |
etd-07162008-172556 |
| Title |
Multivariable Interpolation Problems |
| Degree |
PhD |
| Department |
Mathematics |
| Advisory Committee |
| Advisor Name |
Title |
| Dr. Joseph Ball |
Committee Chair |
| Dr. Michael Williams |
Committee Member |
| Dr. Peter Haskell |
Committee Member |
| Dr. William Greenberg |
Committee Member |
|
| Keywords |
- Noncommutative Fock space
- Drury-Arveson space
- Nevanlinna-Pick interpolation
- Left-tangential operator-argument problem
- Krein space
|
| Date of Defense |
2008-07-07 |
| Availability |
unrestricted |
Abstract
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.
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| Files |
| Filename |
Size |
Approximate Download Time
(Hours:Minutes:Seconds)
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| 28.8 Modem |
56K Modem |
ISDN (64 Kb) |
ISDN (128 Kb) |
Higher-speed Access |
| |
qlfangthesis.pdf |
462.99 Kb |
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