Spectral shift functions and Dirichlet-to-Neumann maps
Spectral Theory
2016-09-28 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
The spectral shift function of a pair of self-adjoint operators is expressed via an abstract operator valued Titchmarsh--Weyl -function. This general result is applied to different self-adjoint realizations of second-order elliptic partial differential operators on smooth domains with compact boundaries, Schr\"{o}dinger operators with compactly supported potentials, and finally, Schr\"{o}dinger operators with singular potentials supported on hypersurfaces. In these applications the spectral shift function is determined in an explicit form with the help of (energy parameter dependent) Dirichlet-to-Neumann maps.
Cite
@article{arxiv.1609.08292,
title = {Spectral shift functions and Dirichlet-to-Neumann maps},
author = {Jussi Behrndt and Fritz Gesztesy and Shu Nakamura},
journal= {arXiv preprint arXiv:1609.08292},
year = {2016}
}