Uniqueness for discrete Schrödinger evolutions
Uniqueness for discrete Schrödinger evolutions
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离散薛定谔演化的独特性
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Karl
中科院分区：
文献类型：
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作者：
Philippe Jaming;Yurii Lyubarskii;E. Malinnikova;Karl
证明了具有有界真实的势的离散含时Schr“odinger方程的解如果在两个不同的时刻快速衰减，则该解是平凡的.对于自由的Shr“odinger算子和具有紧支撑的与时间无关的势的算子，利用基于整函数理论的论证，得到了哈代测不准原理的一个精确模拟.在一般实值含时有界势的情况下，采用加权范数的对数凸性。在后一种情况下，结果不是最佳的。
We prove that if a solution of the discrete time-dependent Schr"odinger equation with bounded real potential decays fast at two distinct times then the solution is trivial. For the free Shr"odinger operator and for operators with compactly supported time-independent potentials a sharp analog of the Hardy uncertainty principle is obtained, using an argument based on the theory of entire functions. Logarithmic convexity of weighted norms is employed in the case of general real-valued time-dependent bounded potentials. In the latter case the result is not optimal.