Oleg Safronov
Absolutely continuous spectrum of a typical Schr\"odinger operator with a slowly decaying potential
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ABSTRACT.  We consider a family of Schroedinger operators of the form $ -\Delta+ t V, $ where $V$ satisfies a certain integral condition. We prove that, for almost every $t$, the absolutely continuous spectrum of this operator is essentially supported by $[0,\infty)$.