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dc.contributor.authorAmaya, Austin J.en_US
dc.date.accessioned2012-05-30en_US
dc.date.accessioned2014-03-14T20:11:50Z
dc.date.available2012-05-30en_US
dc.date.available2014-03-14T20:11:50Z
dc.date.issued2012-04-26en_US
dc.date.submitted2012-05-10en_US
dc.identifier.otheretd-05102012-184739en_US
dc.identifier.urihttp://hdl.handle.net/10919/27636
dc.description.abstractGiven 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,MÃ ) which together form a direct-sum decomposition of L2. In the case where the pair (M,MÃ ) 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,MÃ ). 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,MÃ ) 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.en_US
dc.publisherVirginia Techen_US
dc.relation.haspartAmaya_AJ_D_2012.pdfen_US
dc.rightsI hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Virginia Tech or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.en_US
dc.subjectreproducing kernel Hilbert spacesen_US
dc.subjectHardy spaces over left/right half planeen_US
dc.subjectadmissible Sylvester data seten_US
dc.subjectoperator Sylvester equationen_US
dc.subjectinfinite dimensional zero-pole dataen_US
dc.subjectcontinuous shift semigroupsen_US
dc.subjectLtwo well-posed linear systemsen_US
dc.subjectcontinuous-time linear systemsen_US
dc.titleBeurling-Lax Representations of Shift-Invariant Spaces, Zero-Pole Data Interpolation, and Dichotomous Transfer Function Realizations: Half-Plane/Continuous-Time Versionsen_US
dc.typedissertationen_US
dc.contributor.departmentMathematicsen_US
thesis.degree.namePhDen_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
dc.contributor.committeechairBall, Joseph A.en_US
dc.contributor.committeememberHagedorn, George A.en_US
dc.contributor.committeememberKlaus, Martinen_US
dc.contributor.committeememberRenardy, Michael J.en_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-05102012-184739/en_US


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