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The weak Rayleigh hypothesis and certain properties of systems of metaharmonic functions

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Abstract

We consider a two-dimensional problem of scattering on periodic boundaries. We study properties, such as minimality and property of being a basis, of systems of functions arising during application of the generalized separation-of-variables method. A rigorous formulation of the weak Rayleigh hypothesis, both in the narrow and the wide sense, is given and necessary and sufficient conditions for their validity are obtained.

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Literature cited

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 195, pp. 19–28, 1991.

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Badyukov, V.F. The weak Rayleigh hypothesis and certain properties of systems of metaharmonic functions. J Math Sci 62, 3062–3068 (1992). https://doi.org/10.1007/BF01095677

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Keywords

  • Periodic Boundary
  • Wide Sense
  • Rigorous Formulation
  • Rayleigh Hypothesis
  • Metaharmonic Function