 0377 David Damanik, Rowan Killip
 Halfline Schrodinger Operators With No Bound States
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Feb 28, 03

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Abstract. We consider Sch\"odinger operators on the halfline, both discrete
and continuous, and show that the absence of bound states implies
the absence of embedded singular spectrum. More precisely, in the
discrete case we prove that if $\Delta + V$ has no spectrum
outside of the interval $[2,2]$, then it has purely absolutely
continuous spectrum. In the continuum case we show that if both
$\Delta + V$ and $\Delta  V$ have no spectrum outside
$[0,\infty)$, then both operators are purely absolutely
continuous. These results extend to operators with finitely many
bound states.
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