Scattering matrices and scattering geodesics of locally symmetric spaces
Annales scientifiques de l'École Normale Supérieure, Série 4, Volume 34 (2001) no. 3, p. 441-469
@article{ASENS_2001_4_34_3_441_0,
     author = {Ji, Lizhen and Zworski, Maciej},
     title = {Scattering matrices and scattering geodesics of locally symmetric spaces},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {Ser. 4, 34},
     number = {3},
     year = {2001},
     pages = {441-469},
     doi = {10.1016/s0012-9593(01)01065-5},
     zbl = {1026.53026},
     mrnumber = {1839581},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2001_4_34_3_441_0}
}
Ji, Lizhen; Zworski, Maciej. Scattering matrices and scattering geodesics of locally symmetric spaces. Annales scientifiques de l'École Normale Supérieure, Série 4, Volume 34 (2001) no. 3, pp. 441-469. doi : 10.1016/s0012-9593(01)01065-5. http://www.numdam.org/item/ASENS_2001_4_34_3_441_0/

[1] Borel A., Introduction aux groupes arithmétiques, Hermann, Paris, 1969. | MR 244260 | Zbl 0186.33202

[2] Borel A., Linear algebraic groups, in: Proc. of Symp. in Pure Math., Vol. 9, pp. 3-19. | Zbl 0205.50503

[3] Borel A. Reduction theory for arithmetic subgroups, in: Proc. of Symp. in Pure Math., Vol. 9, pp. 20-25. | Zbl 0213.47201

[4] Borel A., Serre J.-P., Corners and arithmetic groups, Comment. Math. Helv. 48 (1973) 436-491. | MR 387495 | Zbl 0274.22011

[5] Borel A., Tits J., Groupes réductifs, I.H.E.S 27 (1965) 55-150. | Numdam | MR 207712 | Zbl 0145.17402

[6] Duistermaat J., Guillemin V., The spectrum of positive elliptic operators and periodic bicharacteristics, Inv. Math. 29 (1975) 39-79. | MR 405514 | Zbl 0307.35071

[7] Freitag E., Hilbert Modular Forms, Springer-Verlag, 1990. | MR 1050763 | Zbl 0702.11029

[8] Gelfand I.M., Piatetski-Shapiro I.I., Unitary representations in homogeneous spaces with discrete stationary groups, Soviet Math. Dokl. 3 (1962) 1528-1531. | Zbl 0119.27002

[9] Guillemin V., Sojourn times and asymptotic properties of the scattering matrix, Publ. RIMS, Kyoto Univ. 12 (1977) 69-88, (Suppl.). | MR 448453 | Zbl 0381.35064

[10] Guillemin V., Notes on scattering theory, MIT, 1976, unpublished notes.

[11] Harish-Chandra , Automorphic Forms on Semisimple Lie Groups, Lect. Notes in Math., 62, 1968. | Zbl 0186.04702

[12] Hörmander L., Fourier integral operators I, Acta Math. 127 (1971) 79-183. | MR 388463 | Zbl 0212.46601

[13] Hörmander L., The Analysis of Linear Partial Differential Operators, Vol. I, Springer-Verlag, Berlin, 1983.

[14] Hörmander L., The Analysis of Linear Partial Differential Operators, Vol. IV, Springer-Verlag, Berlin, 1985. | Zbl 0601.35001

[15] Ji L., The Weyl upper bound on the discrete spectrum of locally symmetric spaces, J.D.G. 51 (1999) 97-147. | MR 1703605 | Zbl 1036.58028

[16] Ji L., Mcpherson R., Geometry of compactifications of locally symmetric spaces, preprint, 1997. | Zbl 1017.53039

[17] Kuznecov V.N., Petersson's conjecture for cusp forms of weight 0 and Linnik's conjecture: sums of Kloosterman sums, Math. USSR Sbornik 39 (1981). | Zbl 0461.10017

[18] Langlands R., On the Functional Equations Satisfied by Eisenstein Series, Lect. Notes in Math., 544, 1976. | MR 579181 | Zbl 0332.10018

[19] Langlands R., Eisenstein series, the trace formula, and the modern theory of automorphic forms, in: Number Theory, Trace Formula and Discrete Groups, Academic Press, Boston, MA, 1989, pp. 125-155. | MR 993313 | Zbl 0671.10025

[20] Lax P., Phillips R., Scattering Theory for Automorphic Functions, Princeton University Press, 1978. | Zbl 0362.10022

[21] Müller W., The trace class conjecture in the theory of automorphic forms, Ann. of Math. 130 (1989) 473-529. | MR 1025165 | Zbl 0701.11019

[22] Petkov V., Stoyanov L., Geometry of Reflecting Rays and Inverse Spectral Problems, Wiley, 1992. | MR 1172998 | Zbl 0761.35077

[23] Saper L., Tilings and finite energy retractions of locally symmetric spaces, Comment. Math. Helv. 72 (1997) 167-202. | MR 1470087 | Zbl 0890.22003

[24] Selberg A., On discontinuous groups in higher dimensional symmetric spaces, in: Contributions to Function Theory, Tata Inst. of Fund. Res, Bombay, 1960. | MR 130324 | Zbl 0201.36603

[25] Zelditch S., Kuznecov sum formulæ and Szegö limit formulæ on manifolds, Comm. P.D.E. 17 (1992) 221-260. | MR 1151262 | Zbl 0749.58062