Absolutely continuous spectrum of Schrödinger operators with potentials slowly decaying inside a cone |
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Authors: | Oleg Safronov |
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Affiliation: | a Mathematics and Statistics, UNCC, Charlotte, NC 28223, USA b Department of Mathematics, University of Alabama at Birmingham, CH 452, Birmingham, AL 35294-1170, USA |
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Abstract: | For a large class of multi-dimensional Schrödinger operators it is shown that the absolutely continuous spectrum is essentially supported by [0,∞). 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. |
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Keywords: | Schrö dinger operators Absolutely continuous spectrum |
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