Operator-valued bergman inner functions as transfer functions

A. Olofsson

Algebra i analiz, Tome 19 (2007) no. 4, pp. 146-173.

Résumé

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.

Détail

Keywords: Bergman inner function, transfer function, $n$-hypercontraction, wandering subspace, standard weighted Bergman space, discrete time linear system.

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