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Zapiski Nauchnykh Seminarov LOMI, 1991, Volume 195, Pages 19–28 (Mi znsl5022)  
The Weak Rayleigh Hypothesis and some Properties of the Metaharmonic Function Systems

V. F. Badjukov
Full-text PDF (480 kB)
Abstract: 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.
English version:
Journal of Soviet Mathematics, 1992, Volume 62, Issue 6, Pages 3062–3068
DOI: https://doi.org/10.1007/BF01095677
Bibliographic databases:
Document Type: Article
UDC: 517.956:534.26
Language: Russian
Citation: V. F. Badjukov, “The Weak Rayleigh Hypothesis and some Properties of the Metaharmonic Function Systems”, Mathematical problems in the theory of wave propagation. Part 21, Zap. Nauchn. Sem. LOMI, 195, Nauka, St. Petersburg, 1991, 19–28; J. Soviet Math., 62:6 (1992), 3062–3068
Citation in format AMSBIB
\Bibitem{Bad91}
\by V.~F.~Badjukov
\paper The Weak Rayleigh Hypothesis and some Properties of the Metaharmonic Function Systems
\inbook Mathematical problems in the theory of wave propagation. Part~21
\serial Zap. Nauchn. Sem. LOMI
\yr 1991
\vol 195
\pages 19--28
\publ Nauka
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5022}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1158034}
\transl
\jour J. Soviet Math.
\yr 1992
\vol 62
\issue 6
\pages 3062--3068
\crossref{https://doi.org/10.1007/BF01095677}
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