Laplace方程上半平面边值问题中的动态采样

Dynamical sampling in the boundary value problem of Laplace equation in upper half-plane

针对Laplace方程上半平面边值问题,我们研究了利用ϕy∗f的采样来恢复边值f.为了获得采样重构稳定性结果,Shannon采样定理表明采样率必需满足一定条件.在频带有限函数空间中针对采样率不足的情况,通过分析样本扩散矩阵的最小特征值,并利用Remez-Turan不等式避开盲点方法,解决了采样不等式稳定性问题.

For the boundary value problem of Laplace equation in upper half plane,the sampling ofϕy∗f to recover the boundary value f is studied.In order to obtain the stability reconstruction of sampling,Shannon sampling theorem shows that the sampling rate must satisfy certain conditions.The stability of sampling inequality is solved by analyzing the minimum eigenvalue of the sample diffusion matrix and using the Remez-Turan inequality to avoid the blind spot in the case of insufficient sampling rate in the bandlimited function space.