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A logarithmic bound on the location of the poles of the scattering matrix. (English) Zbl 0216.13002


MSC:

35P25 Scattering theory for PDEs
35L99 Hyperbolic equations and hyperbolic systems
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References:

[1] Goodhue, W. L., Dissertation. New York University 1971.
[2] Lax, P. D., & R. S. Phillips, Analytic Properties of the Schrödinger Scattering Matrix, in ”Perturbation Theory and Its Applications in Quantum Mechanics” (C. Wilcox ed.). New York: Wiley 1966, pp. 243–253.
[3] Lax, P. D., & R. S. Phillips, Scattering Theory. New York: Academic Press 1967.
[4] Lax, P. D., & R. S. Phillips, The acoustic equation with an indefinite energy form and the Schrödinger equation. Jr. Functional Anal. 1, 37–83 (1967). · Zbl 0186.16401 · doi:10.1016/0022-1236(67)90026-2
[5] Lax, P. D., & R. S. Phillips, Decaying modes for the wave equation in the exterior of an obstacle. Comm. Pure and Appl. Math. 22, 737–787 (1969). · Zbl 0181.38201 · doi:10.1002/cpa.3160220603
[6] Lax, P. D., & R. S. Phillips, Scattering theory. Rocky Mountain Jr. Math. To appear.
[7] Lax, P. D., C. S. Morawetz, & R. S. Phillips, Exponential decay of solutions of the wave equation in the exterior of a star-shaped obstacle. Comm. Pure and Appl. Math. 16, 477–486 (1963). · Zbl 0161.08001 · doi:10.1002/cpa.3160160407
[8] Ludwig, D., & C. S. Morawetz, The generalized Huyghens’ Principle for reflecting bodies. Comm. Pure and Appl. Math. 22, 188–205 (1969). · Zbl 0187.03304 · doi:10.1002/cpa.3160220602
[9] Phillips, R. S., Perturbation theory for semigroups of linear operators. Trans. Amer. Math. Soc. 74, 199–221 (1953). · doi:10.1090/S0002-9947-1953-0054167-3
[10] Phillips, R. S., A remark on the preceding paper of D. Ludwig and C. S. Morawetz. Comm. Pure and Appl. Math. 22, 207–211 (1969). · Zbl 0167.10103 · doi:10.1002/cpa.3160220205
[11] Ramm, A. G., Regions free of resonance poles in the scattering problem for a three-dimensional potential. Soviet Physics-Doklady 11, 114–116 (1966).
[12] Ramm, A. G., Some theorems on the analytic continuation of the resolvent kernel for the Shrödinger operator with respect to the spectral parameter. Izvestia Akad. Nauk Armyanskoi SSR 3, 443–464 (1968).
[13] Regge, T., Analytic properties of the scattering matrix. Nuovo Cimento 8, 671–679 (1958). · Zbl 0080.41903 · doi:10.1007/BF02815247
[14] Segal, I. E., & Y. Fourès, Causality and analyticity. Trans. Amer. Math. Soc. 78, 385–405 (1955). · Zbl 0064.36805 · doi:10.1090/S0002-9947-1955-0069401-5
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