Convergence of wavelet frame operators as the sampling density tends to infinity

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• 作者：Kangwei Li ^{likangwei9@mail.nankai.edu.cn} ; Wenchang Sun ; ^{sunwch@nankai.edu.cn}
• 关键词：Wavelet frames ; Wavelet transforms ; Frame operators ; Calderó ; n&ndash ; Zygmund operators
• 刊名：Applied and Computational Harmonic Analysis
• 出版年：2012
• 期刊代码：119_10635203
• 类别：cp
• 出版时间：July, 2012
• 卷：33
• 期：1
• 页码：140-147
• 文件大小：173 K

摘要

In this paper, we study the convergence of wavelet frame operators defined by Riemann sums of inverse wavelet transforms. We show that as the sampling density tends to the infinity, the wavelet frame operator tends to the identity or embedding mapping in various operator norms provided the wavelet function satisfies some smoothness and decay conditions. As a consequence, we also get some spanning results of affine systems.