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A Majorant for the Multiplicities of Eigenvalues of the Laplace Operator with Periodic Conditions

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Abstract

In the case of periodic conditions, we find explicit upper estimates in terms of power functions for the multiplicities r n (p) of eigenvalues of the Laplace operator.

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References

  1. A. Erdélyi (ed.), Higher Transcendental Functions. Vol. III (Bateman Manuscript Project, California Inst. Tech., 1981).

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  2. V. L. Vaskevich, “Embedding constants for periodic Sobolev spaces of fractional order,” Sib. Mat. Zh. 49, 1019 (2008) [SiberianMath. J. 49, 806 (2008)].

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  3. V. L. Vaskevich, “The error and guaranteed accuracy of cubature formulas in multidimensional periodic Sobolev spaces,” Sib. Mat. Zh. 55, 971 (2014) [SiberianMath. J. 55, 792 (2014)].

    Article  MathSciNet  MATH  Google Scholar 

  4. S. L. Sobolev, “Convergence of cubature formulas on infinitely differentiable functions,” Dokl. Akad. Nauk SSSR 223, 793 (1975) [Sov.Math., Dokl. 16, 991 (1975)].

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  5. E.W.Weisstein, Sum of Squares Function (MathWorld–AWolframWeb Resource, http://mathworld.wolfram.com/SumofSquaresFunction.html).

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Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    V. L. Vaskevich

  2. Novosibirsk State University, Novosibirsk, 630090, Russia

    V. L. Vaskevich

Authors
  1. V. L. Vaskevich
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Correspondence to V. L. Vaskevich.

Additional information

Original Russian Text © V.L. Vaskevich, 2017, published in Matematicheskie Trudy, 2017, Vol. 20, No. 1, pp. 75–80.

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Vaskevich, V.L. A Majorant for the Multiplicities of Eigenvalues of the Laplace Operator with Periodic Conditions. Sib. Adv. Math. 28, 74–77 (2018). https://doi.org/10.3103/S1055134418010078

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  • DOI: https://doi.org/10.3103/S1055134418010078

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