Scattering matrices and Dirichlet-to-Neumann maps

A general representation formula for the scattering matrix of a scattering system consisting of two self-adjoint operators in terms of an abstract operator valued Titchmarsh–Weyl m-function is proved. This result is applied to scattering problems for different self-adjoint realizations of Schrödinger operators on unbounded domains, Schrödinger operators with singular potentials supported on hypersurfaces, and orthogonal couplings of Schrödinger operators. In these applications the scattering matrix is expressed in an explicit form with the help of Dirichlet-to-Neumann maps. © 2017 The Author(s)

Авторы
Behrndt J.1 , Malamud M.M. 2, 3 , Neidhardt H.4
Издательство
Academic Press Inc.
Номер выпуска
6
Язык
Английский
Страницы
1970-2025
Статус
Опубликовано
Том
273
Год
2017
Организации
  • 1 Institut für Numerische Mathematik, Technische Universität Graz, Steyrergasse 30, Graz, 8010, Austria
  • 2 Institute of Applied Mathematics and Mechanics, National Academy of Science of Ukraine, Dobrovol's'kogo Str. 1, Slavyansk, Donetsk Region 84100, Ukraine
  • 3 Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, 117198, Russian Federation
  • 4 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, Berlin, 10117, Germany
Ключевые слова
Dirichlet-to-Neumann map; Scattering matrix; Schrödinger operator; Titchmarsh–Weyl m-function
Дата создания
19.10.2018
Дата изменения
04.03.2021
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5314/