A logrithmic bound on the location of the poles of the scattering matrix |
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Authors: | Peter D Lax Ralph S Phillips |
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Institution: | 1. New York University, USA 2. Stanford University, USA
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Abstract: | It is shown that the complex poles z of the scattering matrix satisfy the inequality: Im z≧a+b log ¦z¦, b>0, in three instances of classical scattering in three space dimensions described by the wave equation ut t?c2Δu+qu=0. - c and q smooth with c=1 and q=0 for ¦x¦>p, all rays going to infinity, and the energy form positive definite.
- c=1 and q=0 outside of a convex body on which u=0.
- c=1, q bounded and measurable, q=0 for ¦x¦>p, and the energy form not necessarily positive definite.
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