×

Pseudo-laplaciens. II. (French) Zbl 0496.58016


MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
58J10 Differential complexes
53C20 Global Riemannian geometry, including pinching
58C40 Spectral theory; eigenvalue problems on manifolds
30F99 Riemann surfaces

Citations:

Zbl 0489.58034
PDFBibTeX XMLCite
Full Text: DOI Numdam EuDML

References:

[1] [1] , On Cheeger’s inequality λ1 ≥ h2/4, Proc. of Symposia in Pure Mathematics, vol. 36 (1980). · Zbl 0432.58024
[2] [2] , et , Le spectre d’une variété riemannienne, Lecture Notes in Math., 194 (1971). Springer. · Zbl 0223.53034
[3] P. CARTIER, Analyse numérique d’un problème de valeurs propres à haute précision, preprint IHES (1978).0491.10018 · Zbl 0491.10018
[4] J. CHAZARAIN, Formule de Poisson pour les variétés riemanniennes, Inv. Math., 24 (1974), 65-82.0281.3502849 #8062 · Zbl 0281.35028
[5] P. CARTIER et D. HEJHAL, Sur les zéros de la fonction zêta de Selberg, Preprint IHES (1979).0496.10012 · Zbl 0496.10012
[6] E. CODDINGTON et N. LEVINSON, Theory of ordinary differential equations, Mc Graw-Hill (1965).0064.33002 · Zbl 0064.33002
[7] Y. COLIN de VERDIÈRE, Pseudo-Laplaciens I, Ann. Inst. Fourier, 32, 3 (1982), 275-286.0489.5803484k:58221AIF_1982__32_3_275_0 · Zbl 0489.58034
[8] Y. COLIN de VERDIÈRE, Une nouvelle démonstration du prolongement méromorphe des séries d’Eisenstein, C.R.A.S., Paris, 293 (1981), 361-363.0478.3003583a:10038 · Zbl 0478.30035
[9] Y. COLIN de VERDIÈRE, Quasi-modes sur les variétés riemanniennes, Inv. Math., 43 (1977), 15-52.0449.5304058 #18615 · Zbl 0449.53040
[10] H. DONNELLY, On the point spectrum for finite volume symmetric spaces of negative curvature, Comm. P.D.E., 6 (1981), 963-982.0464.3506683a:58090 · Zbl 0464.35066
[11] H. DUISTERMAAT et V. GUILLEMIN, The spectrum of positive elliptic operators and periodic geodesics, Inv. Math., 29 (1975), 39-79.0307.35071 · Zbl 0307.35071
[12] V. GUILLEMIN, Sojourn times and asymptotic properties of the scattering matrix, RIMS Symp., Kyoto, 1976.0381.3506456 #6759 · Zbl 0381.35064
[13] V. GUILLEMIN et R. MELROSE, The Poisson summation formula for manifolds with boundary, Advances in Math., 32 (1979), 204-232.0421.3508280j:58066 · Zbl 0421.35082
[14] L. HÖRMANDER, Fourier integral operators I, Acta Mathematica, 127 (1971), 79-183.0212.4660152 #9299 · Zbl 0212.46601
[15] D. HEJHAL, The Selberg trace formula and the Riemann zêta function, Duke Math. J., 43 (1976), 441-482.0346.1001054 #2591 · Zbl 0346.10010
[16] D. HEJHAL, Some observations concerning eigenvalues of the laplacian and Dirichlet L-series. Recent progress in analytic number theory, Symp. Durham 1979, vol. 2 (1981), 95-110.0457.10009 · Zbl 0457.10009
[17] T. KUBOTA, Elementary theory of Eisenstein series, John Wiley (1973).0268.1001255 #2759 · Zbl 0268.10012
[18] S. LANG, SL2 (R), Addison-Wesley (1975). · Zbl 0311.22001
[19] P. LAX et R. PHILLIPS, Scattering theory for automorphic functions, Ann. of Math. Studies, 87 (1976).0362.1002258 #27768 · Zbl 0362.10022
[20] Y. MOTOHASHI, A note on the mean-value of the Dedekind zêta function of a quadratic field, Math. Ann., 188 (1970), 123-127.0198.0690242 #212 · Zbl 0198.06902
[21] W. MÜLLER, Spectral theory of non-compact manifolds with cusps and a related trace formula, Preprint IHES, déc. 1980.
[22] G. POITOU, Sur les petits discriminants, séminaire D-P-P (1976-1977), exposé n° 6.0393.12010SDPP_1976-1977__18_1_A6_0 · Zbl 0393.12010
[23] H. POTTER et E. TITCHMARSH, The zeros of Epstein zêta functions, Proc. London Math. Soc., 39 (1935), 372-384.0011.3910161.0327.03 · JFM 61.0327.03
[24] B. RANDOL, Cylinders in Riemann surfaces, Comm. Math. Helv., 54 (1979), 1-5.0401.3003680j:30065 · Zbl 0401.30036
[25] E. TITCHMARSH, The theory of Riemann zêta function, Cambridge tracts in Math. and Math. Phys. (ed. 1964).
[26] [26] , Generic properties of eigenfunctions, Amer. J. Math., 98 (1976), 1059-1078. · Zbl 0355.58017
[27] [27] , Russian Math. Surveys, 34 (1979), 79-153.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.