@Article{Główczyk2021,
author = "Główczyk, Anna and Kużel, Sergiusz",
title = "On the S-matrix of Schrödinger operator with nonlocal δ-interaction",
journal = "Opuscula Math.",
year = "2021",
volume = "41",
number = "3",
pages = "413--435",
doi = "https://doi.org/10.7494/OpMath.2021.41.3.413",
url = "https://doi.org/10.7494/OpMath.2021.41.3.413",
abstract = "Schrödinger operators with nonlocal \(\delta\)-interaction are studied with the use of the Lax-Phillips scattering theory methods. The condition of applicability of the Lax-Phillips approach in terms of non-cyclic functions is established. Two formulas for the \(S\)-matrix are obtained. The first one deals with the Krein-Naimark resolvent formula and the Weyl-Titchmarsh function, whereas the second one is based on modified reflection and transmission coefficients. The \(S\)-matrix \(S(z)\) is analytical in the lower half-plane \(\mathbb{C}_{−}\) when the Schrödinger operator with nonlocal \(\delta\)-interaction is positive self-adjoint. Otherwise, \(S(z)\) is a meromorphic matrix-valued function in \(\mathbb{C}_{−}\) and its properties are closely related to the properties of the corresponding Schrödinger operator. Examples of \(S\)-matrices are given.",
keywords = "Lax-Phillips scattering scheme, scattering matrix, \(S\)-matrix, nonlocal \(\delta\)-interaction, non-cyclic function",
issn = "1232-9274"
}