References
Selberg, A., Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series.J. Indian Math. Soc., 20 (1956), 47–87.
Tamagawa, T., On Selberg's trace formula,J. Fac. Sci. Univ. Tokyo, 8 (1960), 363–386.
Gelfand, I. M., Automorphic functions and the theory of representations.Proceedings International Congress of Mathematicians, Stockholm, 1962.
Gelfand, I. M., Graev, M. & Pyatetski-Shapiro I.,Generalized functions, Vol. VI. Moscow, 1966.
Minakshisundaram, S. &Pleijel, Å., Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds.Canad. J. Math., 1 (1949), 242–256.
Helgason, S.,Differential geometry and symmetric spaces. Academic Press, New York, 1962.
—, Fundamental solutions of invariant differential operators on symmetric spaces.Amer. J. Math., 86 (1964) 565–601.
Harish-Chandra, Representations of semisimple Lie groups I.Trans. Amer. Math. Soc., 75 (1953), 185–243.
—, Spherical functions on a semisimple Lie group I.Amer. J. Math., 80 (1958), 241–310.
—, Spherical functions on a semisimple Lie group II.Amer. J. Math., 80 (1958), 553–613.
—, Discrete series for semisimple Lie groups II.Acta Math., 116 (1966), 1–111.
Gindikin, S. &Karpelevic, F., Plancherel measure of Riemannian symmetric spaces of nonpositive curvature.Dokl. Akad. Nauk SSSR, 145 (1962), 252–255;Soviet Math. Dokl., 3 (1962), 962–965.
Bhanu-Murthy, T. S., Plancherel's measure for the factor spaceSL(n, R)/SO(n).Dokl. Akad. Nauk SSSR, 133 (1960), 503–506.
Harish-Chandra, The Plancherel formula for complex semisimple Lie groups.Trans. Amer. Math. Soc., 76 (1954), 485–528.
Itô, S., The fundamental solution of the parabolic equation on a differentiable manifold.Osaka J. Math., 5 (1953), 75–92; 6 (1954), 167–185.
Nelson, E., Analytic vectors.Ann. of Math., 70 (1959), 572–615.
Gangolli, R., Isotropic infinitely divisible measures on symmetric spaces.Acta Math., 111 (1964), 213–246.
Helgason, S., Differential operators on homogeneous spaces.Acta Math., 102 (1959), 239–299.
Harish-Chandra, Invariant eigendistributions on a semisimple Lie, group.Trans. Amer. Math. Soc., 119 (1965) 457–508.
Titchmarsh, E. C.,Theory of, functions. 2nd Edition Oxford University Press, London, 1939.
McKean, P. H. Jr. &Singer, I. M., Curvature and the eigenvalues of the Laplacian.J. Diff. Geom., 1 (1967), 43–70.
Kac, M., Can one hear the shape of a drum?Amer. Math. Monthly, 73 (1966), 1–23.
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Research supported partially by National Science Foundation grant GP-5713 and a fellowship of the Alfred P. Sloan foundation.
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Gangolli, R. Asymptotic behaviour of spectra of compact quotients of certain symmetric spaces. Acta Math. 121, 151–192 (1968). https://doi.org/10.1007/BF02391912
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DOI: https://doi.org/10.1007/BF02391912