The complement of M(a) in H(b)

2020/04/27 by Maria Teresa Nowak Paweł Sobolewski Andrzej Sołtysiak, Sołtysiak, Maria Teresa Nowak Paweł Sobolewski Andrzej
Mathematics · #30H05 #46E22 #47B32 #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2004.12751

openalex publication_date 2020/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let b be a nonextreme function in the unit ball of H^∞ on the unit disk \mathbbD and let a be an outer H^∞ function such that |a|²+|b|²=1 almost everywhere on ∂ \mathbbD. The sufficient and necessary conditions for the orthogonal complement of M(a) in H(b) be finite dimensional has been given by D. Sarason . Here we describe this space explicitly.

Citations

• Which de Branges–Rovnyak spaces are Dirichlet spaces (and vice versa)?

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