On the analytical solution of the linear-fractional Riemann problem

The linear-fractional problem is a generalization of the linear Riemann problem that includes the (non-linear) factorization problem. In case of normal type it can be equivalently reduced to a family of homogeneous linear vector Riemann problems by space foliation and adequate substitutions. Moreover these are equivalent to systems of non-homogeneous Toeplitz equations with special data. The reduced problem is solved by matrix factorization in various cases. Procedures for reduction to these cases are exposed. Various modified problems and generalizations are pointed out. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim