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

FANG Huang; LI Songhua; PENG Hongjie

doi:10.13471/j.cnki.acta.snus.2022A089

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

Research articles | 更新时间：2024-01-25

- Dynamical sampling in the boundary value problem of Laplace equation in upper half-plane
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 63, Issue 1, Pages: 166-172(2024)
- 作者机构：
  
  湖南理工学院数学学院，湖南岳阳 414006
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2022A089
  CLC： O241.5
- Published：25 January 2024，
  
  Published Online：15 November 2023，
  
  Received：14 October 2022，
  
  Accepted：26 February 2023
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方黄,李松华,彭宏杰.Laplace方程上半平面边值问题中的动态采样[J].中山大学学报(自然科学版)(中英文),2024,63(01):166-172.

FANG Huang,LI Songhua,PENG Hongjie.Dynamical sampling in the boundary value problem of Laplace equation in upper half-plane[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2024,63(01):166-172.
方黄,李松华,彭宏杰.Laplace方程上半平面边值问题中的动态采样[J].中山大学学报(自然科学版)(中英文),2024,63(01):166-172. DOI： 10.13471/j.cnki.acta.snus.2022A089.

FANG Huang,LI Songhua,PENG Hongjie.Dynamical sampling in the boundary value problem of Laplace equation in upper half-plane[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2024,63(01):166-172. DOI： 10.13471/j.cnki.acta.snus.2022A089.

摘要

针对Laplace方程上半平面边值问题，我们研究了利用

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=53224936&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=53224932&type=

6.01133299

3.89466691

的采样来恢复边值

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=53224943&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=53224940&type=

2.03200006

2.96333337

. 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 of

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=53224952&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=53224947&type=

7.02733374

4.57200003

to recover the boundary value

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=53224964&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=53224959&type=

2.28600001

3.47133350

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.

关键词

动态采样频带有限函数Remez-Turan不等式Laplace方程

Keywords

dynamic samplingbandlimited functionRemez-Turan inequalityLaplace equation

references

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YU Y S， GU D H， 1997. A note on a lower bound for the smallest singular value［J］. Linear Algebra Appl， 253（1/2/3）： 25-38.

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