On completeness of the system of eigenfunctions of the dirichlet problem for lame equations in the strip

Abstract

© 2015 Nikolai Pleshchinskii, Kristina Stekhina and Dmitrii Tumakov. In the present work, the Dirichlet problem for Lame equations in the strip is considered. A characteristic equation for the problem is obtained. It is shown that the characteristic equation has a denumerable number of simple roots. The conclusion is drawn that any solution to the considered problem can be represented in the form of an eigenfunction series.