Extension of Matrices with Entries in H^{\infty} on Coverings of Riemann Surfaces of Finite Type

TL;DR

This paper proves an extension theorem for matrices with entries in H^{ty} on unbranched coverings of finite type Riemann surfaces, advancing the understanding of bounded holomorphic functions in complex analysis.

Contribution

It extends previous work by establishing an extension theorem for matrices with entries in H^{ty} on specific Riemann surface coverings.

Findings

Established an extension theorem for matrices with entries in H^{ty}

Applied to unbranched coverings of Caratheodory hyperbolic Riemann surfaces

Enhanced understanding of bounded holomorphic functions on complex surfaces

Abstract

In the present paper continuing our previous work we prove an extension theorem for matrices with entries in the algebra of bounded holomorphic functions defined on an unbranched covering of a Caratheodory hyperbolic Riemann surface of finite type.