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

Author: A. Olofsson
Original publication: Algebra i Analiz, tom 19 (2007), nomer 5.
Journal: St. Petersburg Math. J. 19 (2008), 603-623
MSC (2000): Primary 47A48; Secondary 47A15
DOI: https://doi.org/10.1090/S1061-0022-08-01013-3
Published electronically: May 9, 2008
MathSciNet review: 2381937
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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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