A Dirichlet problem in noncommutative potential theory

TL;DR

This paper establishes the solvability of a Dirichlet problem for flat hermitian metrics on Hilbert bundles over compact Riemann surfaces with boundary and proves a factorization result for such metrics on doubly connected domains.

Contribution

It introduces new solvability results for Dirichlet problems in noncommutative potential theory and provides a factorization theorem for flat hermitian metrics.

Findings

Proved solvability of the Dirichlet problem for flat hermitian metrics.

Established a factorization result for flat hermitian metrics on doubly connected domains.

Abstract

We prove the solvability of a Dirichlet problem for flat hermitian metrics on Hilbert bundles over compact Riemann surfaces with boundary. We also prove a factorization result for flat hermitian metrics on doubly connected domains.