Fritz Gesztesy and Mark M. Malamud
Spectral Theory of Elliptic Operators in Exterior Domains
(41K, LaTeX)

ABSTRACT.  We consider various closed (and self-adjoint) extensions of elliptic 
differential expressions of the type $\cA=\sum_{0\le 
|\alpha|,|\beta|\le m}(-1)^\alpha
D^\alpha a_{\alpha, \beta}(x)D^\beta$, $a_{\alpha, \beta}(\cdot)\in 
C^{\infty}({\overline\Omega})$, on smooth (bounded or unbounded) 
domains in $\bbR^n$ with compact boundary. Using the concept of 
boundary triples and operator-valued Weyl-Titchmarsh functions, we 
prove various trace ideal properties of powers of resolvent 
differences of these closed realizations of $\cA$ and derive 
estimates on eigenvalues of certain self-adjoint realizations in 
spectral gaps of the Dirichlet realization.
Our results extend classical theorems due to Visik, Povzner, Birman, and Grubb.