A Generalization of Beurling's Theorem.
by
Yun-Su Kim
University of Toledo

For a Hilbert space K, we define a shift operator S_K on a vector-valued Hardy space H²(W, K) where W is a bounded finitely connected region in the complex plane, whose boundary consists of a finite number of disjoint, analytic, simple closed curves.

We introduce two kinds of quasi-inner functions, and by using quasi-inner functions, we characterize rationally invariant subspaces for the shift operator S_K.

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Date received: November 13, 2007