- 95-273 del Rio R., Simon B., Stolz, G.
- Stability of Spectral Types for Sturm-Liouville Operators
Jun 14, 95
(auto. generated ps),
of related papers
Abstract. For Sturm-Liouville operators on the half line, we show that
the property of having singular, singular continuous, or pure point
spectrum for a set of boundary conditions of positive measure depends
only on the behavior of the potential at infinity. We also prove that
existence of recurrent spectrum implies that of singular spectrum and
that ``almost sure'' existence of $L_2$-solutions implies pure point
spectrum for almost every boundary condition. The same results hold
for Jacobi matrices on the discrete half line.