Exact Solutions for a Class of Matrix Riemann-Hilbert Problems

Amir T. Payandeh Najafabadi • Kucerovsky Kucerovsky


Consider the matrix Riemann-Hilbert problem. In contrast to scalar Riemann-Hilbert problems, a general matrix Riemann-Hilbert problem cannot be solved in term of Sokhotskyi-Plemelj integrals. As far as the authors know, the only known exact solutions known are for a class of matrix Riemann-Hilbert problems with commutative and factorable kernel, and a class of homogeneous problems. This article employs the well known Shannon sampling theorem to provide exact solutions for a class of matrix Riemann-Hilbert problems. We consider matrix Riemann-Hilbert problems in which all the partial indices are zero and the logarithm of the components of the kernels and their nonhomogeneous vectors are functions of exponential type (equivalently, band-limited functions). Then, we develop exact solutions for such matrix Riemann-Hilbert problems. Several well known examples along with a remark on the case of functions not of exponential type are given.




1st Syiah Kuala University Annual International Conference 2011

Proceedings of the Annual International Conference Syiah Kuala University (AIC Unsyiah) is the of... see more