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Modes and quasimodes. (English. Russian original) Zbl 0251.70012
Funct. Anal. Appl. 6, 94-101 (1972); translation from Funkts. Anal. Prilozh. 6, No. 2, 12-20 (1972).

70J10 Modal analysis in linear vibration theory
74K15 Membranes
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
Full Text: DOI
[1] R. Perrin, Selection rules for the splitting of degenerate pairs of natural frequencies of thin circular rings, Acustica,25, No. 2, 69-72 (1971).
[2] R. Thom and H. Levine, Singularities of Differentiable Mappings [Russian translation], Mir, Moscow (1968).
[3] L. D. Landau and E. M. Lifshitz, Quantum Mechanics. Non-relativistic Theory, Addison-Wesley (1958). · Zbl 0081.22207
[4] V. I. Arnol’d, Singularities of smooth mappings, Uspekhi Matem. Nauk,23, No. 1, 3-44 (1968).
[5] R. Thom, Les symetries brisees en physique macroscopique et la mécanique quantique, Publ. IHES (1970).
[6] J. B. Keller and S. I. Rubinow, Asymptotic solution of eigenvalue problems, Ann. Phys.,9, No. 1, 24-75 (1960). · Zbl 0087.43002 · doi:10.1016/0003-4916(60)90061-0
[7] A. I. Baz?, Ya. B. Zel’dovich, and A. M. Perelomov, Scattering, Reactions and Decay in Nonrelativistic Quantum Mechanics, Nauka, Moscow (1971). English translation, Israel Program for Scientific Translations, Ltd., Jerusalem (1969).
[8] V. M. Babich, V. S. Buldyrev, and V. F. Lazutkin, Application of the methods of mathematical diffraction theory to the problem of the asymptotics of the characteristic numbers and functions of Laplace operators, Partial Differential Equations, Sibirsk. Otdel., Akad. Nauk SSSR, Moscow (1970).
[9] V. P. Bykov and L. A. Vainshtein, High Power Electronics,4, Nauka, Moscow (1965).
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