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Gromes, D.

Über die asymptotische Verteilung der Eigenwerte des Laplace-Operators für Gebiete auf der Kugeloberfläche. (German) Zbl 0146.35002

Math. Z. 94, 110-121 (1966).
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Cited in 14 Documents

Keywords:

partial differential equations
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References:

[1] Avakumovi?, V. G.: Über die Eigenfunktionen auf geschlossenen Reimannschen Mannigfaltigkeiten. Math. Zeitschr.65, 327-344 (1956). · Zbl 0070.32601 · doi:10.1007/BF01473886
[2] Bailey, P. B., andF. H. Brownell: Removal of the log factor in the asymptotic estimates of polygonal membrane eigenvalues. Journ. of Math. Anal. and Appl.4, 212-239 (1962). · Zbl 0163.13602 · doi:10.1016/0022-247X(62)90052-5
[3] Brownell, F. H.: An extension of Weyl’s asymptotic law for eigenvalues. Pacific Journ. of Math.5, 483-499 (1955). · Zbl 0066.08602
[4] ? Extended asymptotic eigenvalue distributions for bounded domains inn-space. Journ. of Math. and Mech.6, 119-166 (1957). · Zbl 0084.30901
[5] Carleman, T.: Proprietés asymptotiques des fonctions fondamentales des membranes vibrantes, S.34-44. 8. Skandinavischer Mathematikerkongreß 1934.
[6] Courant, R., u.D. Hilbert: Methoden der mathematischen Physik, Bd.I. Berlin: Springer 1924. · JFM 50.0335.07
[7] Erdély, A., W. Magnus, F. Oberhettinger, andF. G. Tricomi: Bateman manuscript project. Higher transcendental functions, Vol.I. New York-Toronto-London: McGraw-Hill Book Co. 1953.
[8] Fedosov, B. V.: Asymptotic formulas for eigenvalues of the Laplacian in the case of a polygonal region. Dokl. Akad. Nauk. SSSR151, 786-789 (1963) [Soviet Math.4, 1092-1096 (1963)]. · Zbl 0134.09303
[9] ? Asymptotic formulae for the eigenvalues of the Laplace operator in the case of a polyhedron. Dokl. Akad. Nauk. SSSR157, 536-538 (1964) [Soviet Math.5, 988-990 (1964)].
[10] Hardy, G. H., andJ. E. Littlewood: Some problems of Diophantine approximation: The lattice-points of a right-angled triangle. (I) Proc. of the London Math. Soc. Sec. Ser.20, 15-36 (1922). (II) Abhandl. aus dem Math. Seminar der Hamburgischen Universität1, 212-249 (1922). · JFM 48.0197.07 · doi:10.1112/plms/s2-20.1.15
[11] Minakshisundaram, S., andÅ. Pleijel: Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds. Canad. Journ. of Math.1, 242-256 (1949). · Zbl 0041.42701 · doi:10.4153/CJM-1949-021-5
[12] Pleijel, Å.: A study of certain Green’s functions with applications in the theory of vibrating membranes. Arkiv för Matematik2, 553-569 (1954). · Zbl 0055.08801 · doi:10.1007/BF02591229
[13] Pleijel, Å. On Green’s functions and the eigenvalue distribution of the three-dimensional membrane equation. p.222-240. 12.Skandinavischer Mathematikerkongreß 1953.
[14] Pleijel, Å. On the problem of improving Weyl’s law for the asymptotic eigenvalue distribution. Convegno Internazionale sulle Equazioni Lineari alle Derivati Parziali. Trieste 1954. · Zbl 0056.09701
[15] Watson, G. N.: A treatise on the theory of Bessel functions. Cambridge: At the University Press 1962. · Zbl 0105.26801
[16] Weyl, H.: Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung). Math. Ann.71, 441-479 (1912). · JFM 43.0436.01 · doi:10.1007/BF01456804
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