Quasi-inner functions of a generalized Beurling's theorem
Bull. Korean Math. Soc. 2009 Vol. 46, No. 6, 1229-1236
Published online November 1, 2009
Yun-Su Kim
The University of Toledo
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.
Keywords : a generalized Beurling's theorem, Hardy spaces, quasi-inner functions, rationally invariant subspaces
MSC numbers : 47A15, 47A56, 47B37, 47B38
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