On the Anisotropic Wiener-Hopf Operator, Connected with Helmholtze-Sohrodinger Equation

Volume 4, Issue 3, pp 301--309 http://dx.doi.org/10.22436/jmcs.04.03.03

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Authors

S. A. H. Matikolai - Department of Mathematics, Yerevan State University, Yerevan, Armenia H. Jafari - Department of Mathematics, University of Mazandaran, Babolsar, Iran R. Lotfikar - Islamic Azad University Ilam branch

Abstract

In this article, solvability of one the anisotropic Helmholtz-Shrodinger equation with the boundary conditions of the first and second type is investigated in the upper and lower half –space, (x5>0, x5<0), in 5 dimensions. Solvability of these boundary problems reduces to solvability of Rieman- Hilbert boundary problem, in general necessary and sufficient conditions for the correctness of the problem in the Sobolev space are presented as well as explicit formulas for a factorization of the Fourier symbol matrix of the one-medium problem. The solvability analysis is based on the factorization problem of some matrix-function.

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Keywords

• Helmholtz-Shrodinger equation
• Factorization of matrix-function
• Boundary value problem
• Wiener- Hopf equation.

MSC

•  47B35
•  47A53

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