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Functional model for finite rank perturbations

Connections for Women: Harmonic Analysis January 19, 2017 - January 20, 2017

January 20, 2017 (02:30 PM PST - 03:00 PM PST)
Speaker(s): Constanze Liaw (Baylor University)
Location: MSRI: Simons Auditorium
  • finite rank perturbations

  • clark operator

  • harmonic analysis

  • operator theory

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC

Functional Model For Finite Rank Perturbations


The unitary perturbations of a given unitary operator by finite rank d operators can be parametrized by dxd unitary matrices; this generalizes the rank one setting, where the Clark family is parametrized by the scalars on the unit circle. For finite rank perturbations we investigate the functional model of a related class of contractions, as well as a (unitary) Clark operator that realizes such a model representation. We express the adjoint of the Clark operator through a matrix-valued Cauchy integral operator. We determine the matrix-valued characteristic functions of the model (for contractions). In the case of inner characteristic functions results suggest a generalization of the normalized Cauchy transform to the finite rank setting. This presentation is based on joint work with Sergei Treil

27803?type=thumb Liaw Notes 440 KB application/pdf Download
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Functional Model For Finite Rank Perturbations

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