Riemann-Hilbert boundary value problem with piecewise constant transition function (Q2070351)

The authors consider a variant of the Riemann problem. Namely, given a Fuchsian differential equation the corresponding vector bundle is constructed. Then the splitting type is computed. The main result of the paper shows that the splitting type of the holomorphic vector bundle coincides with the partial indices of the corresponding transform matrix function. This result is applied to the factorization of the piecewise constant coefficient of the Riemann-Hilbert boundary value problem, i.e., the determination of the partial indices of the above said coefficient.