Mathematics

Analytical continuation of the Green's function for the equation Helmholtz in the layer

Yu. G. Smirnov, D. V. Valovik

Penza State University, Penza

Abstract: In the article Green's functions first and second kind for the Helmholtz equation in a layer are considered. The opportunity of analytical continuation across positive part of real axis is based upon Riemann-Schwartz principle of symmetry was proved. Correctness of known Green's functions representations in upper half-plane was proved for lower half-plane.

Keywords: Helmholtz equation in a layer, analytical continuation of Green's function.

UDC: 517.6