On the spectral theory of the laplacian on noncompact hyperbolic manifolds

Shmuel Agmon

Journées équations aux dérivées partielles (1987)

  • page 1-16
  • ISSN: 0752-0360

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Agmon, Shmuel. "On the spectral theory of the laplacian on noncompact hyperbolic manifolds." Journées équations aux dérivées partielles (1987): 1-16. <http://eudml.org/doc/93151>.

@article{Agmon1987,
author = {Agmon, Shmuel},
journal = {Journées équations aux dérivées partielles},
keywords = {continuous spectrum; informal lecture; resolvent kernel; generalized eigenfunctions; Eisenstein series},
language = {eng},
pages = {1-16},
publisher = {Ecole polytechnique},
title = {On the spectral theory of the laplacian on noncompact hyperbolic manifolds},
url = {http://eudml.org/doc/93151},
year = {1987},
}

TY - JOUR
AU - Agmon, Shmuel
TI - On the spectral theory of the laplacian on noncompact hyperbolic manifolds
JO - Journées équations aux dérivées partielles
PY - 1987
PB - Ecole polytechnique
SP - 1
EP - 16
LA - eng
KW - continuous spectrum; informal lecture; resolvent kernel; generalized eigenfunctions; Eisenstein series
UR - http://eudml.org/doc/93151
ER -

References

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  1. [1] Agmon, S., Spectral theory of Schrödinger operators on Euclidean and non-Euclidean spaces, Comm. Pure Appl. Math., 39, 1986, pp. S3-S16. Zbl0601.47039
  2. [2] Agmon, S. and Hörmander, L., Asymptotic properties of solutions of differential equations with simple characteristics, J. Analyse Math. 30, 1976, pp. 1-38. Zbl0335.35013MR57 #6776
  3. [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. Zbl0246.10016
  4. [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. Zbl0201.41601
  5. [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. Zbl0335.35004MR47 #9315
  6. [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. Zbl0352.30012
  7. [7] S. Helgason, Eignespaces of the Laplacian ; Integral representations and irreducibility, J. Func. Analysis, 17, 1974, pp. 328-353. Zbl0303.43021MR51 #3353
  8. [8] Hörmander, L., The Anaysis of Linear Partial differential Equations II, Springer-Verlag, New York, 1983. 
  9. [9] Lax, P., and Phillips, R. S., Scattering Theory for Automorpic Functions, Annals of Mathematics Studies 87, Princeton University Press, Princeton, 1976. Zbl0362.10022
  10. [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. Zbl0544.10024
  11. [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. Zbl0033.11702
  12. [12] Mandouvalos, N., The theory of Elisenstein series for Kleinian groups, Contemporary Mathematics, 53, 1986, pp. 357-370. Zbl0628.10031
  13. [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. Zbl0636.58034
  14. [14] Minemurea, K., Eigenfunctions of the Laplacian on a real hyerbolic space, J. Math. Soc. Japan, 27, 1975, pp. 82-105. Zbl0292.35023
  15. [15] Müller, W., Spectral theory for Riemannian manifolds with cusps and related trace formula, Math. Nachtr. 111, 1983, pp. 197-288. Zbl0529.58035MR85i:58121
  16. [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. Zbl0321.30020
  17. [17] Perry, P. A., The Laplace operator on a hyperbolic manifold, I. Spectral and scattering theory, Univ. of Kentucky preprint, 1986. 
  18. [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. Zbl0152.07705
  19. [19] Selberg, A., Discontinuous groups and harmonic analysis, Proc. Internat. Congress of Mathematicians, Stockholm, 1962, pp. 177-189. 
  20. [20] Venkov, A. B., Spectral Theory of Automorphic Functions, Proc. Steklov Inst. of Math. 153, 1981 ; English translation, Amer. Math. Soc., 1982. Zbl0501.10029

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