Preservation of the Absolutely Continuous Spectrum of Schrödinger Equation under Perturbations by Slowly Decreasing Potentials and A.e. Convergence of Integral Operators
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چکیده
X iv :m at h/ 96 10 21 6v 1 [ m at h. SP ] 1 O ct 1 99 6 Abstract. We prove new criteria of stability of the absolutely continuous spectrum of one-dimensional Schrödinger operators under slowly decaying perturbations. As applications, we show that the absolutely continuous spectrum of the free and periodic Schrödinger operators is preserved under perturbations by all potentials V (x) satisfying |V (x)| ≤ C(1 + x)− 23−ǫ. The main new technique includes an a.e. convergence theorem for a class of integral operators.
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تاریخ انتشار 1998