Riemann Boundary Value Problem of Non-Normal Type on the Infinite Straight Line

DOI: 10.4236/am.2013.48165   PDF   HTML     4,715 Downloads   6,016 Views   Citations


Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions have been widely investigated in [1-8]. The main ap- proach is to use the decomposition of polyanalytic functions and their generalization to transform the boundary value problems to their corresponding boundary value problems for analytic functions. Recently, inverse Riemann BVPs for generalized analytic functions or bianalytic functions have been investigated in [9-12].
In this paper, we consider a kind of Riemann BVP of non-normal type on the infinite straight line and discuss the solvable conditions and the general solution for it.

Share and Cite:

L. Cao, "Riemann Boundary Value Problem of Non-Normal Type on the Infinite Straight Line," Applied Mathematics, Vol. 4 No. 8, 2013, pp. 1226-1230. doi: 10.4236/am.2013.48165.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] M. B. Balk, “Polyanalytic Functions,” Akademie Verlag, Berlin, 1991.
[2] H. Begehr and A. Kumar, “Boundary Value Problems for the Inhomogeneous Polyanalytic Equation I,” Analysis: International Mathematical Journal of Analysis and Its Application, Vol. 25, No. 1, 2005, pp. 55-71.
[3] D. Jinyuan and W. Yufeng, “On Boundary Value Prob lems of Polyanalytic Functions on the Real Axis,” Com plex Variables, Vol. 48, No. 6, 2003, pp. 527-542. doi:10.1080/0278107031000103412
[4] B. F. Fatulaev, “The Main Haseman Type Boundary Value Problem for Metaanalytic Function in the Case of Circular Domains,” Mathematical Modelling and Analy sis, Vol. 6, No. 1, 2001, pp. 68-76.
[5] J. K. Lu, “Boundary Value Problems for Analytic Func tions,” World Scientific, Singapore City, 1993.
[6] A. S. Mshimba, “A Mixed Boundary Value Problem for Polyanalytic Function of Order n in the Sobolev Space Wn, p(D),” Complex Variables, Vol. 47, No. 12, 2002, pp. 278-1077.
[7] N. I. Muskhelishvili, “Singular Integral Equations,” World Scientific, Singapore City, 1993.
[8] W. Yufeng and D. Jinyuan, “Hilbert Boundary Value Problems of Polyanalytic Functions on the Unit Circum ference,” Complex Variables and Elliptic Equations, Vol. 51, No. 8-11, 2006, pp. 923-943. doi:10.1080/17476930600667692
[9] L. Xing, “A Class of Periodic Riemann Boundary Value Inverse Problems,” Proceedings of the Second Asian Mathematical Conference, Nakhon Ratchasima, 17-20 October 1995, pp. 397-400.
[10] M. H. Wang, “Inverse Riemann Boundary Value Prob lems for Generalized Analytic Functions,” Journal of Ningxia University of Natural Resources and Life Sci ences Education, Vol. 27, No. 1, 2006, pp. 18-24.
[11] X. Q. Wen and M. Z. Li, “A Class of Inverse Riemann Boundary Value Problems for Generalized Holomorphic Functions,” Journal of Mathematical, Vol. 24, No. 4, 2004, pp. 457-464.
[12] L. X. Cao, P.-R. Li and P. Sun, “The Hilbert Boundary Value Problem With Parametric Unknown Function on Upper Half-Plane,” Mathematics in Practice and Theory, Vol. 42, No. 2, 2012, pp. 189-194.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.