| 李登峰,马俊.局部域上Gabor紧框架的特征[J].数学年刊A辑,2015,36(1):13~20 |
| 局部域上Gabor紧框架的特征 |
| Characterization of Gabor Tight Frames on Local Fields |
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| DOI： |
| 中文关键词: 紧框架, Gabor框架, 局部域 |
| 英文关键词:Tight frame, Gabor frame, Local field |
| 基金项目:本文受到国家自然科学基金(No. 61471410)和武汉纺织大学学科创新团队建设基金(No.201401023)的资助. |
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| 中文摘要: |
| 主要讨论局部域上的~Gabor~紧框架.首先, 建立局部域上~Gabor~系$\{\chi_{m}(bx)g(x-u(n)a)\}_{m,n\in P}$构成$L^{2}(K)$上紧框架的特征.
其次, 给出~Gabor~系$\{\chi_{m}(bx)g(x-u(n)a)\}_{m,n\in P}$成为$L^{2}(K)$上标准正交基的充要条件. |
| 英文摘要: |
| This paper deals with Gabor tight frames on local fields. Firstly, the characterizations for
the Gabor system $\{\chi_{m}(bx)g(x-u(n)a)\}_{m,n\in P}$ to be a tight frame in
$L^{2}(K)$ are established. Sceondly, some necessary and sufficient conditions
for the Gabor system $\{\chi_{m}(bx)g(x-u(n)a)\}_{m,n\in P}$ to be an orthonormal basis
in $L^{2}(K)$ are presented. |
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