# Spectral Theory of Elliptic Operators in Exterior Domains - Mathematics > Spectral Theory

Abstract: We consider various closed and self-adjoint extensions of ellipticdifferential expressions of the type $\cA=\sum {0\le |\alpha|,|\beta|\lem}-1^\alpha D^\alpha a {\alpha, \beta}xD^\beta$, $a {\alpha,\beta}\cdot\in C^{\infty}{\overline\Omega}$, on smooth bounded orunbounded domains in $\bbR^n$ with compact boundary. Using the concept ofboundary triples and operator-valued Weyl-Titchmarsh functions, we provevarious trace ideal properties of powers of resolvent differences of theseclosed realizations of $\cA$ and derive estimates on eigenvalues of certainself-adjoint realizations in spectral gaps of the Dirichlet realization.Our results extend classical theorems due to Visik, Povzner, Birman, andGrubb.

Author: Fritz Gesztesy, Mark M. Malamud

Source: https://arxiv.org/