Existence of resonances in potential scattering

Communications on Pure and Applied Mathematics

Volumn 49, Issue 12, 1996, Pages 1271-1280

  Sá Barreto, Antônio ^a   Zworski, Maciej ^b  

^a PURDUE UNIVERSITY   (United States)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030522814     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-0312(199612)49:12<1271::aid-cpa2>3.3.co;2-i     Document Type: Article

References (17)

1. Bañuelos, R., and Sá Barreto, A., On the heat trace of Schrödinger operators, Comm. Partial Differential Equations 20(11-12), 1995, pp. 2153-2164.
2. 3, Ann. Sci. École Norm. Sup. (4) 14(1), 1981, pp. 27-39.
3. Davies, E. B., Heat Kernels and Spectral Theory, Cambridge University Press, Cambridge, 1990.
4. Froese, R., Asymptotic distribution of resonances in one dimension, preprint, 1994.
5. Klopp, F., and Zworski, M., Generic simplicity of resonances, preprint, 1995.
6. Lax, P., and Phillips, R., Decaying modes for the wave equation in the exterior of an obstacle, Comm. Pure Appl. Math. 22, 1969, pp. 737-787.
7. Melrose, R. B., Scattering theory and the trace of the wave group, J. Funct. Anal. 45(1), 1982, pp. 29-40.
8. Melrose, R. B., Geometric Scattering Theory, Stanford Lectures, Cambridge University Press, Cambridge, 1995.
9. Menzala, G. P., and Schonbek, T., Scattering frequencies for the wave equation with a potential term, J. Funct. Anal. 55(3), 1984, pp. 297-322.
10. Petras, S. V., Continuous dependence of poles of the scattering matrix on coefficients of an elliptic operator, Trudy Mat. Inst. Steklov. 159, 1983, pp. 132-136.
11. Sá Barreto, A., and Zworski, M., Existence of resonances in three dimensions, Comm. Math. Phys. 173(2), 1995, pp. 401-415.
12. Simon, B., Schrödinger semigroups, Bull. Amer. Math. Soc. (N.S.) 7(3), 1982, pp. 447-526.
13. Varopoulos, N. Th., Hardy-Littlewood theory for semigroups, J. Funct. Anal. 63, 1985, pp. 240-260.
14. Zworski, M., Distribution of poles for scattering on the real line, J. Funct. Anal. 73(2), 1987, pp. 277-296.
15. Zworski, M., Sharp polynomial bounds on the number of scattering poles, Duke Math. J. 59(2), 1989, pp. 311-323.
16. Zworski, M., Sharp polynomial bounds on the number of scattering poles of radial potentials, J. Funct. Anal. 82(2), 1989, pp. 370-403.
17. Zworski, M., Counting scattering poles, pp. 301-331 in: Spectral and Scattering Theory, Lecture Notes in Pure and Applied Mathematics No. 161, Dekker, New York, 1994.