Operator-valued Bergman inner functions as transfer functions

Olofsson, A.

doi:10.1090/S1061-0022-08-01013-3

Operator-valued Bergman inner functions as transfer functions
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by A. Olofsson

St. Petersburg Math. J. 19 (2008), 603-623

DOI: https://doi.org/10.1090/S1061-0022-08-01013-3

Published electronically: May 9, 2008

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Abstract:

An explicit construction characterizing the operator-valued Bergman inner functions is given for a class of vector-valued standard weighted Bergman spaces in the unit disk. These operator-valued Bergman inner functions act as contractive multipliers from the Hardy space into the associated Bergman space, and they have a natural interpretation as transfer functions for a related class of discrete time linear systems. This points to a new interaction between the fields of invariant subspace theory and mathematical systems theory.

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