The Weak Rayleigh Hypothesis and some Properties of the Metaharmonic Function Systems

The present work considers a two-dimensional scalar problem of scattering on the periodic boundaries. The properties of function systems arising at realization of the generalized method of separation of variables such as minimality and baseness are investigated. Rigorous statements of the weak Rayleigh hypothesis and also the weak Rayleigh hypothesis in the wide-sense and the weak Rayleigh hypothesis in the narrow-sense are given. The necessary and sufficient conditions of their validity are received.