Title page for ETD etd-07162008-172556

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
Ball, Joseph A. Committee Chair
Greenberg, William Committee Member
Haskell, Peter E. Committee Member
Williams, Michael Committee Member
  • Noncommutative Fock space
  • Drury-Arveson space
  • Nevanlinna-Pick interpolation
  • Left-tangential operator-argument problem
  • Krein space
Date of Defense 2008-07-07
Availability unrestricted
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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