A canonical decomposition of strong L²-functions

2018/05/17 by In Sung Hwang, Hwang, In Sung, Woo Young Lee +1
Mathematics · #30H10 #30J05 #46E40 #47B35 #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1805.06574

openalex publication_date 2018/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to establish a canonical decomposition of operator-valued strong L²-functions by the aid of the Beurling-Lax-Halmos Theorem which characterizes the shift-invariant subspaces of vector-valued Hardy space. This decomposition invites us to coin a new notion of the "Beurling degree" of the inner function. Eventually, we establish a deep connection between the spectral multiplicity of the model operator and the Beurling degree of the corresponding characteristic function.

Citations

• On two problems concerning linear transformations in hilbert space

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