Sampling solutions of Schro¨dinger equations on combinatorial graphs
Sampling solutions of Schro¨dinger equations on combinatorial graphs
复制标题
组合图上薛定谔方程的采样解
DOI：
10.1109/sampta.2015.7148855
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
I. Pesenson
中科院分区：
文献类型：
--
作者：
I. Pesenson
我们考虑图G上的函数，它在时间-∞；t<；；∞的演化由右边带有组合拉普拉斯算子的Schrödinger型方程控制。对于给定的S顶点子集，我们计算一个截止频率ω>；0，使得具有PW<SUB>ω</SUB>(G)中初始数据的柯西问题的解完全由S x{kπ/ω}上的样本决定，其中kεN。
We consider functions on a graph G whose evolution in time - ∞ <; t <; ∞ is governed by a Schrödinger type equation with a combinatorial Laplace operator on the right side. For a given subset S of vertices of G we compute a cut-off frequency ω > 0 such that solutions to a Cauchy problem with initial data in PW<sub>ω</sub> (G) are completely determined by their samples on S x {kπ /ω}, where k ε N. It is shown that in the case of a bipartite graph our results are sharp.