2017
Том 69
№ 6

All Issues

Scattering Theory for 0-Perturbed $\mathcal{P}\mathcal{T}$ -Symmetric Operators

Hrod A. I., Kuzhel' S. A.

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Abstract

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 PTPT -symmetric operators is described in terms of the corresponding $\mathcal{C}$ -matrix (scattering matrix).

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 8, pp 1180-1202.

Citation Example: Hrod A. I., Kuzhel' S. A. Scattering Theory for 0-Perturbed $\mathcal{P}\mathcal{T}$ -Symmetric Operators // Ukr. Mat. Zh. - 2013. - 65, № 8. - pp. 1059–1079.

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