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Translation Representations And Scattering By Two Intervals, Palle Jorgensen, Steen Pedersen, Feng Tian
Translation Representations And Scattering By Two Intervals, Palle Jorgensen, Steen Pedersen, Feng Tian
Mathematics and Statistics Faculty Publications
Studying unitary one-parameter groups in Hilbert space (U(t), H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L2-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U(t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator and scattering matrix. We illustrate our results in the Lax-Phillips model where (U(t), H) represents an acoustic wave equation …