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Existence of resonances in potential scattering

1996; Wiley; Volume: 49; Issue: 12 Linguagem: Inglês

10.1002/(sici)1097-0312(199612)49

1097-0312

Antônio Sá Barreto, Maciej Zworski,

Spectral Theory in Mathematical Physics

Communications on Pure and Applied MathematicsVolume 49, Issue 12 p. 1271-1280 Existence of resonances in potential scattering Antônio Sá Barreto, Corresponding Author Antônio Sá Barreto Dept. of Mathematics, Purdue University, West Lafayette, IN 47907Dept. of Mathematics, Purdue University, West Lafayette, IN 47907Search for more papers by this authorMaciej Zworski, Maciej Zworski Dept. of Mathematics, University of Toronto, Toronto, Ontario, M5S 3G3, CanadaSearch for more papers by this author Antônio Sá Barreto, Corresponding Author Antônio Sá Barreto Dept. of Mathematics, Purdue University, West Lafayette, IN 47907Dept. of Mathematics, Purdue University, West Lafayette, IN 47907Search for more papers by this authorMaciej Zworski, Maciej Zworski Dept. of Mathematics, University of Toronto, Toronto, Ontario, M5S 3G3, CanadaSearch for more papers by this author First published: December 1996 https://doi.org/10.1002/(SICI)1097-0312(199612)49:12 3.0.CO;2-7Citations: 21AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Bibliography 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. 10.1080/03605309508821166 Web of Science®Google Scholar 2 Colin de Verdière, Y. Une formule de traces pour l'opérateur de Schrödinger dans R3, Ann. Sci. École Norm. Sup. (4) 14(1), 1981, pp. 27–39. Google Scholar 3 Davies, E. B., Heat Kernels and Spectral Theory, Cambridge University Press, Cambridge, 1990. Google Scholar 4 Froese, R., Asymptotic distribution of resonances in one dimension, preprint, 1994. Google Scholar 5 Klopp, F., and Zworski, M., Generic simplicity of resonances, preprint, 1995. Google Scholar 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. 10.1002/cpa.3160220603 Web of Science®Google Scholar 7 Melrose, R. B., Scattering theory and the trace of the wave group. J. Funct. Anal. 45(1), 1982, pp. 29–40. 10.1016/0022-1236(82)90003-9 Web of Science®Google Scholar 8 Melrose, R. B., Geometric Scattering Theory, Stanford Lectures, Cambridge University Press, Cambridge, 1995. Google Scholar 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. 10.1016/0022-1236(84)90002-8 Web of Science®Google Scholar 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. Google Scholar 11 Sá Barreto, A., and Zworski, M., Existence of resonances in three dimensions. Comm. Math. Phys. 173(2), 1995, pp. 401–415. 10.1007/BF02101240 Web of Science®Google Scholar 12 Simon, B., Schrödinger semigroups. Bull. Amer. Math. Soc. (N.S.) 7(3), 1982, pp. 447–526. 10.1090/S0273-0979-1982-15041-8 Web of Science®Google Scholar 13 Varopoulos, N. Th., Hardy-Littlewood theory for semigroups, J. Funct. Anal. 63, 1985, pp. 240–260. 10.1016/0022-1236(85)90087-4 Web of Science®Google Scholar 14 Zworski, M., Distribution of poles for scattering on the real line. J. Funct. Anal. 73(2), 1987, pp. 277–296. 10.1016/0022-1236(87)90069-3 Web of Science®Google Scholar 15 Zworski, M., Sharp polynomial bounds on the number of scattering poles. Duke Math. J. 59(2), 1989, pp. 311–323. 10.1215/S0012-7094-89-05913-9 Web of Science®Google Scholar 16 Zworski, M., Sharp polynomial bounds on the number of scattering poles of radial potentials. J. Funct. Anal. 82(2), 1989, pp. 370–403. 10.1016/0022-1236(89)90076-1 Web of Science®Google Scholar 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. Web of Science®Google Scholar Citing Literature Volume49, Issue12December 1996Pages 1271-1280 ReferencesRelatedInformation