Title page for ETD etd-05102012-184739


Type of Document Dissertation
Author Amaya, Austin J.
Author's Email Address amaya@vt.edu
URN etd-05102012-184739
Title Beurling-Lax Representations of Shift-Invariant Spaces, Zero-Pole Data Interpolation, and Dichotomous Transfer Function Realizations: Half-Plane/Continuous-Time Versions
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Ball, Joseph A. Committee Chair
Hagedorn, George A. Committee Member
Klaus, Martin Committee Member
Renardy, Michael J. Committee Member
Keywords
  • reproducing kernel Hilbert spaces
  • Hardy spaces over left/right half plane
  • admissible Sylvester data set
  • operator Sylvester equation
  • infinite dimensional zero-pole data
  • continuous shift semigroups
  • Ltwo well-posed linear systems
  • continuous-time linear systems
Date of Defense 2012-04-26
Availability unrestricted
Abstract
Given a full-range simply-invariant shift-invariant subspace M of the vector-valued L2 space on the unit circle, the classical Beurling-Lax-Halmos (BLH) theorem obtains a unitary operator-valued function W so that M may be represented as the image of of the Hardy space H2 on the disc under multiplication by W. The work of Ball-Helton later extended this result to find a single function representing a so-called dual shift-invariant pair of subspaces (M,M×) which together form a direct-sum decomposition of L2. In the case where the pair (M,M×) are finite-dimensional perturbations of the Hardy space H2 and its orthogonal complement, Ball-Gohberg-Rodman obtained a transfer function realization for the representing function W; this realization was parameterized in terms of zero-pole data computed from the pair (M,M×). Later work by Ball-Raney extended this analysis to the case of nonrational functions W where the zero-pole data is taken in an infinite-dimensional operator theoretic sense. The current work obtains analogues of these various results for arbitrary dual shift-invariant pairs (M,M×) of the L2 spaces on the real line; here, shift-invariance refers to invariance under the translation group. These new results rely on recent advances in the understanding of continuous-time infinite-dimensional input-state-output linear systems which have been codified in the book by Staffans.
Files
  Filename       Size       Approximate Download Time (Hours:Minutes:Seconds) 
 
 28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access 
  Amaya_AJ_D_2012.pdf 579.51 Kb 00:02:40 00:01:22 00:01:12 00:00:36 00:00:03

Browse All Available ETDs by ( Author | Department )

dla home
etds imagebase journals news ereserve special collections
virgnia tech home contact dla university libraries

If you have questions or technical problems, please Contact DLA.