The aim of the present work is to develop the scattering theory for 0-perturbed \( \mathcal{P}\mathcal{T} \) -symmetric operators by using the Lax–Phillips method. The presence of a stable \( \mathcal{C} \) -symmetry leading to the property of selfadjointness (with proper choice of the inner product) for these \( \mathcal{P}\mathcal{T} \) -symmetric operators is described in terms of the corresponding S -matrix (scattering matrix).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 8, pp. 1059–1079, August, 2013.
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Hrod, A.I., Kuzhel’, S.O. Scattering Theory for 0-Perturbed \( \mathcal{P}\mathcal{T} \) -Symmetric Operators. Ukr Math J 65, 1180–1202 (2014). https://doi.org/10.1007/s11253-014-0851-9
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DOI: https://doi.org/10.1007/s11253-014-0851-9