 08182 Fritz Gesztesy and Mark M. Malamud
 Spectral Theory of Elliptic Operators in Exterior Domains
(41K, LaTeX)
Oct 9, 08

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We consider various closed (and selfadjoint) 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 operatorvalued WeylTitchmarsh 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 selfadjoint realizations in
spectral gaps of the Dirichlet realization.
Our results extend classical theorems due to Visik, Povzner, Birman, and Grubb.
 Files:
08182.tex