Scattering theory for perturbed stratified media |
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Authors: | T Christiansen |
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Institution: | (1) Department of Mathematics, University of Missouri, 65211 Columbia, MO, USA |
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Abstract: | We study the operatorH = -c
2
x,y)Μx,y)∇ · Μ
-1
(x,y)∇, wherec andΜ are perturbations of functionsc
0(y) andΜ
0(y) which depend only on the one-dimensional variabley. In particular, we study the spatial asymptotics of limε↺0(H - (λ +iε)2)-1 applied to functions which have compact support or are otherwise well-behaved at infinity and relate the scattering matrix
to the asymptotics of the generalized eigenfunctions. We then prove a trace formula for the operatorH in terms of the scattering phase, and, in a very special situation, use the trace formula to find spectral asymptotics forH.
Partially supported by an NSF Postdoctoral Fellowship and the University of Missouri Research Board. |
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Keywords: | |
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