Extension of matrices with entries in $H^{\infty }$ on coverings of Riemann surfaces of finite type

DOI10.1090/S1061-0022-10-01101-5zbMath1204.30041arXiv0801.1720OpenAlexW2963991505MaRDI QIDQ3586757

Alexander Brudnyi

Publication date: 1 September 2010

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.1720

zbMATH Keywords

bounded holomorphic functionBezout equationcorona problemCarathéodory hyperbolicityRiemann surface of finite type

Mathematics Subject Classification ID

Spaces of bounded analytic functions of one complex variable (30H05) Hardy spaces (30H10) Algebras of analytic functions of one complex variable (30H50)

Related Items (3)

Projective free algebras of bounded holomorphic functions on infinitely connected domains ⋮ Corona theorem for \(H^{\infty }\) on covering of Riemann surfaces of finite type ⋮ Corona Problem for H ∞ on Riemann Surfaces

Cites Work

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• The Corona theorem for Denjoy domains
• Critical points of Green's function, harmonic measure, and the corona problem
• Grauert- and Lax-Halmos-type theorems and extension of matrices with entries in \(H^{\infty}\).
• A uniqueness property for \(H^{\infty}\) on coverings of projective manifolds
• A new construction of Riemann surfaces with corona
• Projections in the space \(H^{\infty}\) and the corona theorem for subdomains of coverings of finite bordered Riemann surfaces
• Corona theorem for \(H^{\infty }\) on covering of Riemann surfaces of finite type
• Interpolations by bounded analytic functions and the corona problem
• Matrix-valued corona theorem for multiply connected domains
• The Corona Theorem for Domains whose Boundary Lies in a Smooth Curve
• Extension Problem to an Invertible Matrix
• Holomorphic Functions of Slow Growth on Nested Covering Spaces of Compact Manifolds
• Bounded Holomorphic Functions on Finite Riemann Surfaces

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