Spectral asymptotics for the Dirichlet Laplacian with a Neumann window via a Birman-Schwinger analysis of the Dirichlet-to-Neumann operator.
A. Hänel, and T. Weidl. Functional Analysis and Operator Theory for Quantum Physics, EMS Series of Congress Reports, J. Dittrich, et al. (eds.), (2017)
Abstract
"In the present article we will give a new proof of the ground state asymptotics of the Dirichlet Laplacian with a Neumann window acting on functions which are defined on a two-dimensional infinite strip or a three-dimensional infinite layer. The proof is based on the analysis of the corresponding Dirichlet-to-Neumann operator as a first order classical pseudo-differential operator. Using the explicit representation of its symbol we prove an asymptotic expansion as the window length decreases."
%0 Journal Article
%1 hanel2017spectral
%A Hänel, André
%A Weidl, Timo
%D 2017
%J Functional Analysis and Operator Theory for Quantum Physics, EMS Series of Congress Reports, J. Dittrich, et al. (eds.)
%K iadm from:elkepeter asymptotics Hänel Weidl Spectral
%P 315 - 352
%T Spectral asymptotics for the Dirichlet Laplacian with a Neumann window via a Birman-Schwinger analysis of the Dirichlet-to-Neumann operator.
%X "In the present article we will give a new proof of the ground state asymptotics of the Dirichlet Laplacian with a Neumann window acting on functions which are defined on a two-dimensional infinite strip or a three-dimensional infinite layer. The proof is based on the analysis of the corresponding Dirichlet-to-Neumann operator as a first order classical pseudo-differential operator. Using the explicit representation of its symbol we prove an asymptotic expansion as the window length decreases."
@article{hanel2017spectral,
abstract = {"In the present article we will give a new proof of the ground state asymptotics of the Dirichlet Laplacian with a Neumann window acting on functions which are defined on a two-dimensional infinite strip or a three-dimensional infinite layer. The proof is based on the analysis of the corresponding Dirichlet-to-Neumann operator as a first order classical pseudo-differential operator. Using the explicit representation of its symbol we prove an asymptotic expansion as the window length decreases."},
added-at = {2021-10-13T13:52:26.000+0200},
author = {Hänel, André and Weidl, Timo},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/20e1f49c7962599f662210ebaff44b50b/mathematik},
interhash = {0e936fa8a9fa8b397cdce8f023e68e69},
intrahash = {0e1f49c7962599f662210ebaff44b50b},
journal = {Functional Analysis and Operator Theory for Quantum Physics, EMS Series of Congress Reports, J. Dittrich, et al. (eds.)},
keywords = {iadm from:elkepeter asymptotics Hänel Weidl Spectral},
language = {English},
pages = {315 - 352},
timestamp = {2021-10-13T11:52:26.000+0200},
title = {Spectral asymptotics for the Dirichlet Laplacian with a Neumann window via a Birman-Schwinger analysis of the Dirichlet-to-Neumann operator.},
year = 2017
}
