从快照重构抽象薛定谔、扩散和波动型方程的解
Reconstruction of solutions to abstract Schrodinger, diffusion, and wave-type equations from snapshots
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中文总结 AI 辅助
本文证明，通过足够多的快照，可用类似香农公式的简单公式重构薛定谔型方程的带限解，并推广到扩散和波动型方程，且公式与算子无关。
中文摘要 AI 辅助
研究表明，如果已知一个薛定谔型方程的某个解的“足够多”快照（样本），且该解在适当意义下是带限的，则可以通过一个类似于带限信号香农公式的简单公式重构该解。此外，结果证明，利用薛定谔型方程带限解的快照，可以重构一些相关扩散型和波动型方程的带限解。有趣的是，重构公式本质上与定义这些方程的算子无关。
英文摘要
It is shown that if one knows "sufficiently many" snapshots (samples) from an individual solution of a Schrödinger-type equation-which is bandlimited in an appropriate sense-then the solution can be reconstructed by a simple formula similar to the Shannon formula for bandlimited signals. Furthermore, results demonstrate that by using snapshots of bandlimited solutions of a Schrödinger-type equation, one can reconstruct bandlimited solutions of some relevant diffusion- and wave-type equations. Interestingly, the reconstruction formulas are essentially independent of the operators defining the equations.
