A generalization of frame perturbation in Hilbert subspaces and its application to wavelet subspaces

ZHAO Ping; LIU Guizhong; ZHAO Chun

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A generalization of frame perturbation in Hilbert subspaces and its application to wavelet subspaces

机译：Hilbert子空间中帧扰动的推广及其在小波子空间中的应用

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摘要

A perturbation theorem for frames in a Hilbert space is obtained, which is a generalization of a result by Christensen. Based on this general result, an irregular sampling theorem for frames in wavelet subspaces is established, which has a previous result as a special case.

机译：获得了希尔伯特空间中框架的摄动定理，这是克里斯滕森对结果的推广。基于该一般结果，建立了小波子空间中帧的不规则采样定理，在特殊情况下具有先前的结果。

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来源
《Science in China. Series F, Information Sciences》 |2003年第2期|p.151-159|共9页
作者
ZHAO Ping; LIU Guizhong; ZHAO Chun;
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作者单位

Department of Information and Communication Engineering, Xi'an Jiaotong University, Xi'an 710049 , China;

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原文格式 PDF
正文语种 eng
中图分类自然科学总论;情报学、情报工作;
关键词
frame perturbation; sampling; wavelets;

机译：帧扰动;采样;小波;

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2. Perturbations of invariant subspaces of operators with Hilbert-Schmidt Hermitian components [J] . Gil Michael Archiv der Mathematik . 2015,第5期

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3. Multivariate FMRAs and FMRA frame wavelets for reducing subspaces of L~2 (R~d) [J] . Feng-Ying Zhou, Yun-Zhang Li Journal of Mathematics of Kyoto University . 2010,第1期

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4. Isometric isomorphism between a Hilbert space of sequence and a general wavelet subspace [C] . Zhang Zhi-Guo Proceedings of 2011 International Conference on Wavelet Analysis and Pattern Recognition . 2011

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5. Analysis of small and large perturbations of matrix subspaces [D] . Macinnes, Craig Scott 1995

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7. Wavelet frames for (not necessarily reducing) affine subspaces II: The structure of affine subspaces [O] . Gu Qing, Han Deguang 2011

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A generalization of frame perturbation in Hilbert subspaces and its application to wavelet subspaces

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