×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.