Abstract
Let K 0 be a free Feller operator and let KΣ: be the corresponding operator with Dirichlet boundary conditions on Γ = ℝn \ Σ. The scattering system established by k 0,KΣ} is complete, i.e., the wave operators exist and are complete if the singularity region Γ has finite capacity. One consequence is the stability of the absolutely continuous spectra of K0 and KΣ respectively. Such sets can be unbounded, which yields a non-local freedom of perturbation in the scattering theory. Kato-Feller potentials can be included.
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van Casteren, J., Demuth, M. (1998). Completeness of scattering systems with obstacles of finite capacity. In: Gohberg, I., Mennicken, R., Tretter, C. (eds) Differential and Integral Operators. Operator Theory: Advances and Applications, vol 102. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8789-2_4
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DOI: https://doi.org/10.1007/978-3-0348-8789-2_4
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