Geodesic
The Weak Rayleigh Hypothesis and some Properties of the Metaharmonic Function Systems
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 21, Tome 195 (1991), pp. 19-28 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{ZNSL_1991_195_a2,
     author = {V. F. Badjukov},
     title = {The {Weak} {Rayleigh} {Hypothesis} and some {Properties} of the {Metaharmonic} {Function} {Systems}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {19--28},
     year = {1991},
     volume = {195},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1991_195_a2/}
}
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V. F. Badjukov. The Weak Rayleigh Hypothesis and some Properties of the Metaharmonic Function Systems. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 21, Tome 195 (1991), pp. 19-28. http://geodesic.mathdoc.fr/item/ZNSL_1991_195_a2/