The theory of Riemann boundary value problem for analytic functions of one complex variable and singular integral equations that are equivalent to it has been extensively studied in the literature. For classical books on this topic see [7, 12, 13] and for an actual overview of them the reader is directed to the monograph by Estrada and Kanwal [6], and the references therein. In the more recent ...

We characterize the biorthogonal polynomials that appear in the theory of coupled random matrices via a Riemann-Hilbert problem. Our Riemann-Hilbert problem is different from the ones that were proposed recently by Ercolani and McLaughlin, Kapaev, and Bertola et al. We believe that our formulation may be tractable to asymptotic analysis.

The solution of the Riemann problem was a building block for general Cauchy problems in conservation laws. A Cauchy problem is approximated by a series of Riemann problems in many numerical schemes. But, since the structure of the Riemann solution holds locally in time only, and, furthermore, a Riemann solution is not piecewise constant in general, there are several fundamental issues in this a...