A Generalization of Beurling's Theorem and Quasi-Inner Functions

Details A Generalization of Beurling's Theorem and Quasi-Inner Functions A Generalization of Beurling's Theorem and Quasi-Inner Functions

2006-12-27

arxiv.org/abs/math/0612790v3

Mathematics

Functional Analysis

Scientific paper

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator $S_K$ on a vector-valued Hardy space $H^{2}(\Omega,K)$ 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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