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

2006/12/27 by Yun-Su Kim, Kim, Yun-Su
Mathematics · #17C65 #42B30 #42B35 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA #msc:17C65 #msc:42B30 #msc:42B35

paper · pdf · doi:10.48550/arxiv.math/0612790

openalex publication_date 2006/12/27 · arxiv created 2008/01/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 H²(Ω,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.

Citations

• On two problems concerning linear transformations in hilbert space

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