Phase space localized functions in the Dunkl setting

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• 作者：Saifallah Ghobber
• 关键词：Time–frequency concentration ; Localized functions ; Dunkl ; Gabor transform ; Localization operator ; Spectrogram
• 刊名：Journal of Pseudo-Differential Operators and Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：7
• 期：4
• 页码：571-593
• 全文大小：528 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：None Assigned
• 出版者：Birkh盲user Basel
• ISSN：1662-999X
• 卷排序：7

文摘

Time–frequency analysis plays a central role in signal analysis, because signals that have highly concentrated time–frequency content are used in many applications. The uncertainty principle in Fourier analysis sets a limit to the possible simultaneous concentration of a function and its Dunkl transform. To localize signals in the time–frequency plane we use time–frequency localization operators in the Dunkl setting to measure their time–frequency content on some subset of finite measure. Then, using eigenfunctions of these operators, which are maximally time–frequency concentrated, we prove a characterization of functions that are time–frequency concentrated in the region of interest, and we obtain approximation inequalities for such functions using a finite linear combination of eigenfunctions.