Resonance wave expansions: Two hyperbolic examples

Communications in Mathematical Physics

Volumn 212, Issue 2, 2000, Pages 323-336

  Christiansen, T ^a   Zworski, M ^b  

^a UNIVERSITY OF MISSOURI   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034349028     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200000211     Document Type: Review

References (23)

1. 1. Beyer, H.: On the completeness of the quasinormal modes of the Pöschl-Teller potential. Commun. Math. Phys. 204, 397-423 (1999)
2. 2. Epstein, Ch.: Unpublished
3. 3. Erdélyi, A. et. al.: Higher Transcendental Functions. Vol. I. New York: McGraw-Hill Book Company, Inc., 1953
4. 4. Gérard, Ch.: Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes. Mém. Soc. Math. France (N.S.) 31, (1988)
5. 5. Guillopé, L.: Pöschl-Teller potentials and Laplacians on hyperbolic spaces. Unpublished
6. 6. Guillopé, L.: Sur la distribution des longuers des géodésiques fermées d'une surface compacte à bord totalement géodésique. Duke Math. J. 53, 827-848 (1986)
7. 7. Guillopé, L. and Zworski, M.: Upper bounds on the number of resonances for non-compact Riemann surfaces. J. Funct. Anal. 129 (2), 364-389 (1995)
8. 8. Guillopé, L. and Zworski, M.: Scattering asymptotics for Riemann surfaces. Ann. Math. 145, 597-660 (1997)
9. 9. Ikawa, M.: On the poles of the scattering matrix for two strictly convex obstacles. J. Math. Kyoto Univ. 23, 127-194 (1983)
10. 10. Ikawa, M.: Private communication
11. 11. Iwaniec, H. and Sarnak, P.: L∞ norms of eigenfunctions of arithmetic surfaces. Ann. of Math. 141, 301-320 (1995)
12. 12. Lax, P. and Phillips, R.: Scattering Theory. New York: Academic Press, 1st edition 1969, 2nd edition 1989
13. 13. Luke, Y.: The Special functions and their approximations. Vol. 1. New York: Academic Press, 1969
14. 14. Müller, W.: Spectral geometry and scattering theory for certain complete surfaces of finite volume. Invent. Math. 109, 265-305 (1992)
15. 15. Sá Barreto, A. and Zworski, M.: Distribution of resonances for spherical black holes. Math. Res. Lett. 4, 103-121 (1997)
16. 16. Sarnak, P.: Arithmetic quantum chaos. The Schur lectures (1992, Tel Aviv). Israel Math. Conf. Proc. 8, 183-236 (1995)
17. 17. Soffer, A. and Weinstein, M.: Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations. Invent. Math. 136, 9-74 (1999)
18. 18. Tang, S.-H. and Zworski, M.: From quasimodes to resonances. Math. Res. Lett. 5 3, 261-272 (1998)
19. 19. Tang, S.-H. and Zworski, M.: Resonance expansions of scattered waves. Preprint, 1999
20. 20. Titchmarsh, E.C.: The Theory of the Riemann zeta-function. Second edition. Oxford: Clarendon Press, 1986
21. 21. Vainberg, B.R.: Exterior elliptic problems that depend polynomially on the spectral parameter, and the asymptotic behavior for large values of the time of the solutions of nonstationary problems. (Russian) Mat. Sb. (N.S.) 92 134, 224-241 (1973)
22. 22. Vainberg, B.R.: Asymptotic methods in equations of mathematical physics. London: Gordon and Breach, 1989
23. 23. Zworski, M.: Resonances in physics and geometry. Notices Amer. Math. Soc. 46, 319-328 (1999)