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On elements of the Lax-Phillips scattering scheme for ρ-perturbations of an abstract wave equation

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Abstract

We give the definition of ρ-perturbations of an abstract wave equation. As a special case, this definition includes perturbations with compact support for the classical wave equation. By using the Lax-Phillips method, we study scattering of “ρ-perturbed” systems and establish some properties of corresponding scattering matrices.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    S. A. Kuzhel’

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  1. S. A. Kuzhel’
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 12, pp. 1615–1629, December, 1998.

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Kuzhel’, S.A. On elements of the Lax-Phillips scattering scheme for ρ-perturbations of an abstract wave equation. Ukr Math J 50, 1844–1859 (1998). https://doi.org/10.1007/BF02514201

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  • DOI: https://doi.org/10.1007/BF02514201

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