On the spectral theory of the laplacian on noncompact hyperbolic manifolds
Journées équations aux dérivées partielles (1987), article no. 17, 16 p.
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     author = {Agmon, Shmuel},
     title = {On the spectral theory of the laplacian on noncompact hyperbolic manifolds},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {17},
     pages = {1--16},
     publisher = {Ecole polytechnique},
     year = {1987},
     mrnumber = {89c:58128},
     zbl = {0636.58037},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_1987____A17_0/}
}
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Agmon, Shmuel. On the spectral theory of the laplacian on noncompact hyperbolic manifolds. Journées équations aux dérivées partielles (1987), article  no. 17, 16 p. http://www.numdam.org/item/JEDP_1987____A17_0/

[1] Agmon, S., Spectral theory of Schrödinger operators on Euclidean and non-Euclidean spaces, Comm. Pure Appl. Math., 39, 1986, pp. S3-S16. | Zbl

[2] Agmon, S. and Hörmander, L., Asymptotic properties of solutions of differential equations with simple characteristics, J. Analyse Math. 30, 1976, pp. 1-38. | MR | Zbl

[3] Elstrodt, J., Die Resolvente zum Eigenwert problem der automorphen Formen in der hyperbolischen Ebene, I, II, III, Math. ann. 203, 1973, pp. 295-330 ; Math. Z., 132, 1973 pp. 99-134 ; Math. Ann. 208, 1974, pp. 99-132. | Zbl

[4] Faddeev, L. D., Expansion in eigenfunctirons of the Laplace operator in the fundamental domain of a discrete group on the Lobachevski plane, Trudy Moscow Mat. Obsch. 17, 1967, pp. 323-350 ; English transl., Trans. Moscow Math. Soc., 17, 1967, pp. 357-386. | Zbl

[5] Faddeev, L. D. and Pavlov, B. S., Scattering theory and automorphic functions, Seminar of the Steklov Mathematical Institute of Leningrad 27, 1972, pp. 161-193. | MR | Zbl

[6] Fay, J. D., Fourier coefficeints of the resolvent for a Fuchsian group, J. Für die Reine und Angewandte Math., 293-294, 1977, pp. 143-203. | Zbl

[7] S. Helgason, Eignespaces of the Laplacian ; Integral representations and irreducibility, J. Func. Analysis, 17, 1974, pp. 328-353. | MR | Zbl

[8] Hörmander, L., The Anaysis of Linear Partial differential Equations II, Springer-Verlag, New York, 1983.

[9] Lax, P., and Phillips, R. S., Scattering Theory for Automorpic Functions, Annals of Mathematics Studies 87, Princeton University Press, Princeton, 1976. | Zbl

[10] Lax, P., and Phillips, R. S., Translation representation for automorphic solutions of the wave equation in non-Euclidean spaces, I, II, III, Comm. Pure Appl. Math. 37, 1984, pp. 303-324, pp. 779-813 and 38, 1985, pp. 179-208. | Zbl

[11] Maass, H., Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 121, 1949, pp. 141-183. | Zbl

[12] Mandouvalos, N., The theory of Elisenstein series for Kleinian groups, Contemporary Mathematics, 53, 1986, pp. 357-370. | Zbl

[13] Mazzeo, R. R., and Melrose, R. B., Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature, M. I. T. preprint, 1986.

[14] Minemurea, K., Eigenfunctions of the Laplacian on a real hyerbolic space, J. Math. Soc. Japan, 27, 1975, pp. 82-105. | Zbl

[15] Müller, W., Spectral theory for Riemannian manifolds with cusps and related trace formula, Math. Nachtr. 111, 1983, pp. 197-288. | MR | Zbl

[16] Patterson, S. J., The Laplacian operator on a Riemann surface, I, II, III, Comp. Math. 31, 1975, pp. 83-107 ; 32, 1976, pp. 71-112 ; 33, 1976, pp. 227-259. | Numdam | Zbl

[17] Perry, P. A., The Laplace operator on a hyperbolic manifold, I. Spectral and scattering theory, Univ. of Kentucky preprint, 1986.

[18] Roelcke, W., Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene, I, II, Math. ann. 167, 1966, pp. 292-337 ; 168, 1967, pp. 261-324. | Zbl

[19] Selberg, A., Discontinuous groups and harmonic analysis, Proc. Internat. Congress of Mathematicians, Stockholm, 1962, pp. 177-189.

[20] Venkov, A. B., Spectral Theory of Automorphic Functions, Proc. Steklov Inst. of Math. 153, 1981 ; English translation, Amer. Math. Soc., 1982. | Zbl