Bulletin of the American Mathematical Society

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Book Information:

Author: Pierre H. Bérard
Title: Spectral geometry: Direct and inverse problems
Additional book information: with an appendix by G. Besson. Lecture Notes in Mathematics, Vol. 1207, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1986, xiii+272 pp., $23.40. ISBN 3-540-16788-9.

Yves Colin de Verdière, Spectre du laplacien et longueurs des géodésiques périodiques. I, II, Compositio Math. 27 (1973), 83–106; ibid. 27 (1973), 159–184 (French). MR 348798

Isaac Chavel, Riemannian geometry, 2nd ed., Cambridge Studies in Advanced Mathematics, vol. 98, Cambridge University Press, Cambridge, 2006. A modern introduction. MR 2229062, DOI 10.1017/CBO9780511616822

Jean Delsarte, Sur le gitter fuchsien, C. R. Acad. Sci. Paris 214 (1942), 147–179 (French). MR 7769

S. Minakshisundaram and Å. Pleijel, Some properties of the eigenfunctions of the Laplace-operator on Riemannian manifolds, Canad. J. Math. 1 (1949), 242–256. MR 31145, DOI 10.4153/cjm-1949-021-5

H. P. McKean, Selberg’s trace formula as applied to a compact Riemann surface, Comm. Pure Appl. Math. 25 (1972), 225–246. MR 473166, DOI 10.1002/cpa.3160250302

A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.) 20 (1956), 47–87. MR 88511

[CDV] Y. Colin de Verdière, Spectre du Laplacien et longueurs des géodésiques périodiques. I, II, Compositio Math. 27 (1973), 83-106; 159-184. MR 0348798




[CH] I. Chavel, Eigenvalues in Riemannian geometry, Academic Press, New York, 1984. MR 2229062




[D] J. Delsarte, Sur le gitter Fuchsien, C. R. Acad. Sci. Paris 241 (1942), 147-149. MR 7769




[M-P] S. Minakshisundaram and øA. Pleijel, Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds, Canad. J. Math. 1 (1949), 242-256. MR 31145




[MK] H. P. McKean, Selberg's trace formula as applied to a compact Riemann surface, Comm. Pure Appl. Math. 25 (1972), 225-246. MR 473166




[S] A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric spaces with applications to Dirichlet series, J. Indian Math. Soc. 20 (1956), 47-87. MR 88511