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Scattering theory for 0-perturbed \(\mathcal{PT}\)-symmetric operators. (English. Ukrainian original) Zbl 1323.47006

Ukr. Math. J. 65, No. 8, 1180-1202 (2014); translation from Ukr. Mat. Zh. 65, No. 8, 1059-1079 (2013).
Summary: The aim of the present work is to develop the scattering theory for 0-perturbed \(\mathcal{PT}\)-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 \(\mathcal{PT}\)-symmetric operators is described in terms of the corresponding \(S\)-matrix (scattering matrix).

MSC:

47A40 Scattering theory of linear operators
81Q12 Nonselfadjoint operator theory in quantum theory including creation and destruction operators
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References:

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