ANALYTICAL GREEN’S FUNCTION EXTENSION FOR HELMHOLZ EQUATION IN A LAYER

Smirnov Yury Gennadyevich, Doctor of physico-mathematical sciences, professor, head of sub-department
of mathematics and supercomputer modeling, Penza State University , Smirnov@Penzadom.ru
Valovik Dmitry Viktorovich, Candidate of physico-mathematical sciences, associate professor, sub-department of mathematics and supercomputer modeling, Penza State University , necco@mail.ru

517.6

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.

Helmholtz equation in a layer, analytical continuation of Green’s function.