Projections in the Space H^∞ and the Corona Theorem for Coverings of Bordered Riemann Surfaces

2001/10/14 by Alexander Brudnyi, Brudnyi, Alexander · 2 citations
Mathematics · #30D15 #32F05 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #msc:30D15 #msc:32F05

paper · pdf · doi:10.48550/arxiv.math/0110149

arxiv created 2001/10/14 · openalex publication_date 2001/10/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a non-compact connected Riemann surface of finite type, and R⊂⊂ M be a relatively compact domain such that H₁(M,\Z)=H₁(R,\Z). Let R\longrightarrow R be a covering. We study the algebra H^∞(U) of bounded holomorphic functions defined in some domains U⊂ R. Our main result is a Forelli type theorem on projections in H^∞(\Di).

Cited by

• Extension of Matrices with Entries in H^∞ on Coverings of Riemann Surfaces of Finite Type
• A Grauert Type Theorem and Extension of Matrices with Entries in H^∞

Related

• Corona Theorem for H^∞ on Coverings of Riemann Surfaces of Finite Type
• A Uniqueness Property for H^∞ on Coverings of Projective Manifolds
• Extension of Matrices with Entries in H^∞ on Coverings of Riemann Surfaces of Finite Type
• On Stable Rank of \mathbf H^∞ on Coverings of Finite Bordered Riemann Surfaces
• Another proof of the corona theorem