Geodesic
A majorant for the multiplicities of eigenvalues of the Laplace operator with periodic conditions
Matematičeskie trudy, Tome 20 (2017) no. 1, pp. 75-80 
V. L. Vaskevich. A majorant for the multiplicities of eigenvalues of the Laplace operator with periodic conditions. Matematičeskie trudy, Tome 20 (2017) no. 1, pp. 75-80. http://geodesic.mathdoc.fr/item/MT_2017_20_1_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii. Ellipticheskie i avtomorfnye funktsii. Funktsii Lame i Mate, Nauka, M., 1967

[2] Vaskevich V. L., “Konstanty vlozheniya periodicheskikh prostranstv Soboleva drobnogo poryadka”, Sib. matem. zhurn., 49:5 (2008), 1019–1027 | Zbl

[3] Vaskevich V. L., “Pogreshnost i garantirovannaya tochnost kubaturnykh formul v mnogomernykh periodicheskikh prostranstvakh Soboleva”, Sib. matem. zhurn., 55:5 (2014), 971–988

[4] Sobolev S. L., Skhodimost kubaturnykh formul na beskonechno differentsiruemykh funktsiyakh, Izbrannye trudy, v. 1, Uravnenie matematicheskoi fiziki. Vychislitelnaya matematika i kubaturnye formuly, Izd-vo In-ta matematiki, filial «Geo» Izd-va SO RAN, Novosibirsk, 2003

[5] Weisstein E. W., Sum of Squares Function, MathWorld–A Wolfram Web Resource, http://mathworld.wolfram.com/SumofSquaresFunction.html