# QUASI-INNER FUNCTIONS OF A GENERALIZED BEURLING'S THEOREM

• Kim, Yun-Su (Department of Mathematics The University of Toledo)
• Published : 2009.11.30

#### Abstract

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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