In mathematics, especially spectral theory, Weyl's law describes the asymptotic behavior of eigenvalues of the Laplace–Beltrami operator. This description was discovered in 1911 (in the case) by Hermann Weyl for eigenvalues for the Laplace–Beltrami operator acting on functions that vanish at the boundary of a bounded domain . In particular, he proved that the number, , of Dirichlet eigenvalues (counting their multiplicities) less than or equal to satisfies where is a volume of the unit ball in . In 1912 he provided a new proof based on variational methods.
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| - Асимптотическая формула Вейля (ru)
- Weyl law (en)
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| - In mathematics, especially spectral theory, Weyl's law describes the asymptotic behavior of eigenvalues of the Laplace–Beltrami operator. This description was discovered in 1911 (in the case) by Hermann Weyl for eigenvalues for the Laplace–Beltrami operator acting on functions that vanish at the boundary of a bounded domain . In particular, he proved that the number, , of Dirichlet eigenvalues (counting their multiplicities) less than or equal to satisfies where is a volume of the unit ball in . In 1912 he provided a new proof based on variational methods. (en)
- Асимптотическая формула Вейля связывает объём риманова многообразия с асимптотическим поведением собственных значений его лапласиана. (ru)
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| - In mathematics, especially spectral theory, Weyl's law describes the asymptotic behavior of eigenvalues of the Laplace–Beltrami operator. This description was discovered in 1911 (in the case) by Hermann Weyl for eigenvalues for the Laplace–Beltrami operator acting on functions that vanish at the boundary of a bounded domain . In particular, he proved that the number, , of Dirichlet eigenvalues (counting their multiplicities) less than or equal to satisfies where is a volume of the unit ball in . In 1912 he provided a new proof based on variational methods. (en)
- Асимптотическая формула Вейля связывает объём риманова многообразия с асимптотическим поведением собственных значений его лапласиана. (ru)
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