06-159 Oleg Safronov, G\"unter Stolz

Absolutely continuous spectrum of Schr\"odinger operators with potentials slowly decaying inside a cone (294K, pdf) May 15, 06

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Abstract. This is a revised version of mp-arc 05-316. For a large class of multi-dimensional Schr\"odinger operators it is shown that the absolutely continuous spectrum is essentially supported by $[0,\infty)$. We require slow decay and mildly oscillatory behavior of the potential in a cone and can allow for arbitrary non-negative bounded potential outside the cone. In particular, we do not require the existence of wave operators. The result and method of proof extends previous work by Laptev, Naboko and Safronov.

Files: 06-159.src( 06-159.keywords , coneJMAArev.pdf.mm )