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Spectres et groupes cristallographiques. I: Domaines euclidiens. (Spectra and crystallographic groups. I: Euclidean domains). (French) Zbl 0434.35068


MSC:

35P05 General topics in linear spectral theory for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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References:

[1] Bérard, P., Besson, G.: Spectres et Groupes Cristallographiques II: Domaines Sphériques, Ann. Institut Fourier à paraître (1980) · Zbl 0426.35073
[2] Bérard, P.: On the number of lattice points in some domains. Comm. in Partial Diff. Eq.3, 335-347 (1978) · Zbl 0391.10032
[3] Berger, M., Gauduchon, P., Mazet, E.: Le spectre d’une variété riemannienne, Lecture Notes in Mathematics, no 194. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0223.53034
[4] Bourbaki, N.: Groupes et algèbres de Lie, Chapitres 4 à 6. Act. Scient. et Industrielles 1337. Paris: Hermann 1968 · Zbl 0483.22001
[5] Duistermaat, J., Guillemin, V.: The spectrum of positive elliptic operators with periodic bicharacteristics. Inventiones Math.29, 39-79 (1975) · Zbl 0307.35071
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[8] Hejahl, D.: The Selberg trace formula and the Riemann zeta function. Duke Math. J.43, 441-482 (1976) · Zbl 0346.10010
[9] Keller, J., Rubinow, S.: Asymptotic solutions of eigenvalue problems. Annals of Physics,9, 24-75 (1960) · Zbl 0087.43002
[10] Melrose, R.: Weyl’s conjecture for manifolds with concave boundary. Proceedings of Symposia in Pure Math. no 36, Amer. Math. Soc. à paraître · Zbl 0436.58024
[11] McKean, H., Singer, I.M.: Curvature and the eigenvalues of the laplacian. Journal Differential Geom.1, 43-69 (1967) · Zbl 0198.44301
[12] Polya, G., Szegö, G.: Isoperimetric inequalities in mathematical physics. Annals of Mathematical Studies no 27. Princeton: Princeton Univers. Press 1966
[13] Pinsky, M.: The Eigenvalues of an equilateral triangle, à paraître dans Siam Journal of Mathematical Analysis · Zbl 0462.35072
[14] Serre, J.P.: Cours d’arithmétique. Paris: Presses Universitaires de France 1970
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