Operator-valued Bergman Inner Functions as Transfer Functions
نویسنده
چکیده
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. Let U , X , and Y be general not necessarily separable complex Hilbert spaces, and let A ∈ L(X ), B ∈ L(U ,X ), C ∈ L(X ,Y), and D ∈ L(U ,Y) be bounded linear operators. Let n ≥ 1 be an integer. We shall consider operator-valued analytic functions of the form (0.1) W (z) = D + zC ( n ∑
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