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All Journal Proceedings of Annual International Conference Syiah Kuala University - Life Sciences & Engineering Chapter
Amir T. Payandeh Najafabadi
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Exact solutions for a class of matrix Riemann-Hilbert problems Amir T. Payandeh Najafabadi; . Kucerovsky
Proceedings of The Annual International Conference, Syiah Kuala University - Life Sciences & Engineering Chapter Vol 1, No 2 (2011): Engineering
Publisher : Syiah Kuala University

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Abstract

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. 
Co-Authors . Kucerovsky