International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 17, Pages 2821-2840

Riemann boundary value problem for hyperanalytic functions

Ricardo Abreu Blaya,1 Juan Bory Reyes,1 and Dixan Peña Peña1

1Faculty of Mathematics and Informatics, University of Holguín, Holguín 80100, Cuba
2Department of Mathematics, University of Oriente, Santiago de Cuba 90500, Cuba
3Department of Mathematical Analysis, Ghent University, Galglaan 2, Ghent 9000, Belgium

Received 23 February 2005

Copyright © 2005 Ricardo Abreu Blaya et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We deal with Riemann boundary value problem for hyperanalytic functions. Furthermore, necessary and sufficient conditions for solvability of the problem are derived. At the end the explicit form of general solution for singular integral equations with a hypercomplex Cauchy kernel in the Douglis sense is established.