Absolutely continuous spectrum of the Schrödinger operator with a potential representable as a sum of three functions with special properties
Absolutely continuous spectrum of the Schrödinger operator with a potential representable as a sum of three functions with special properties
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薛定谔算子的绝对连续谱，具有可表示为具有特殊性质的三个函数之和的潜力
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
O. Safronov
中科院分区：
文献类型：
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作者：
O. Safronov
我们考虑一类依赖于一个真实的参数的薛定谔算子族，并证明了对于该参数的几乎每一个值，其绝对连续谱都覆盖正半线。该模型中的势可以表示为三项之和。这个和既不快速衰减，也不快速改变其符号或具有相对于角度变量的导数。
We consider a family of Schrodinger operators depending on a real parameter and prove that the absolutely continuous spectrum covers the positive half-line for almost every value of the parameter. The potentials in this model are representable as a sum of three terms. This sum is neither fast decaying, nor it rapidly changes its sign or has derivatives with respect to the angular variables.