Analytic solution to the problem of the behavior of a collisional plasma in a half-space in an external alternating electric field

An exact solution of the linear problem of the collision plasma behaviour in half space in external alternating electric field is obtained. The specular boundary conditions are used. In the space of distributions the eigenvectors for the corresponding characteristic equation are found and their spectrum is investigated. The theorem about the expansion of the solution in eigenvectors is proved. The exact formula for calculation of the discrete mode is presented explicitly.