- 98-39 Renger W.
- Limiting absorption principle for singularly perturbed operators
(69K, LATeX 2e)
Jan 28, 98
(auto. generated ps),
of related papers
Abstract. Given an operator $H_1$ for which a limiting absorption principle holds,
we study operators $H_2$ which are produced by perturbing $H_1$ in the
sense that the difference between some powers of the resolvents
is compact. We show that (except for possibly a discrete set of
eigenvalues) a limiting absorption principle holds for $H_2$.
We apply this theory to study potential and
domain perturbations of Feller operators. While our theory mostly
reproduces known results in the case of potential perturbations,
for domain perturbations we get results which appear to be new.