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
方黄 1李松华 1彭宏杰1
作者信息
- 1. 湖南理工学院数学学院, 湖南 岳阳 414006
- 折叠
摘要
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.
Abstract
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 sam-pling,Shannon sampling theorem shows that the sampling rate must satisfy certain conditions.The sta-bility 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.
关键词
动态采样/频带有限函数/Remez-Turan不等式/Laplace方程Key words
dynamic sampling/bandlimited function/Remez-Turan inequality/Laplace equation引用本文复制引用
基金项目
湖南省自然科学基金(2020JJ4330)
湖南省教育厅重点项目(19A196)
出版年
2024
国家科技期刊平台
NSTL
维普
万方数据