TY  - JOUR
ID  - Główczyk2021
LB  - Główczyk2021
AU  - Główczyk, Anna
AU  - Kużel, Sergiusz
TI  - On the S-matrix of Schrödinger operator with nonlocal δ-interaction
ST  - On the S-matrix of Schrödinger operator with nonlocal δ-interaction
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2021
VL  - 41
IS  - 3
SP  - 413
EP  - 435
DO  - https://doi.org/10.7494/OpMath.2021.41.3.413
UR  - https://doi.org/10.7494/OpMath.2021.41.3.413
AB  - 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.
KW  - Lax-Phillips scattering scheme
KW  - scattering matrix
KW  - \(S\)-matrix
KW  - nonlocal \(\delta\)-interaction
KW  - non-cyclic function
SN  - 1232-9274
ER  -