Lower bounds on the number of scattering poles under lines parallel to the real axis. (English) Zbl 0822.35105

Summary: We provide lower bounds in slab domains on the number of scattering poles, generated by two different types of periodic non-hyperbolic rays. For the first one all eigenvalues of the corresponding Poincaré map are equal to one and for the second one two of the eigenvalues are equal to one and two are different from one. In the second case we find also the closest to the real axis “line of poles”.


35P25 Scattering theory for PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
78A45 Diffraction, scattering
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