A Generalization of Beurling's Theorem and Quasi-Inner Functions
Abstract
We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator SK on a vector-valued Hardy space H2(,K) is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions, and quasi-inner divisors.
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