Extra-strong uncertainty principles in relation to phase derivative for signals in Euclidean spaces

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• 作者：Pei Dang^a ; ^{pdang@must.edu.mo" class="auth_mail" title="E-mail the corresponding author} ; Tao Qian^b ; ^{fsttq@umac.mo" class="auth_mail" title="E-mail the corresponding author} ; Yan Yang^c ; ^{mathyy@sina.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Signals in Euclidean spaces ; Hilbert transform ; Uncertainty principle ; Phase derivative ; Amplitude derivative
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：437
• 期：2
• 页码：912-940
• 全文大小：515 K

文摘

This paper devotes to studying uncertainty principles of Heisenberg type for signals defined on Rⁿ${\mathbf{R}}^n$ taking values in a Clifford algebra. For real-para-vector-valued signals possessing all first-order partial derivatives we obtain two uncertainty principles of which both correspond to the strongest form of the Heisenberg type uncertainty principles for the one-dimensional space. The lower-bounds of the new uncertainty principles are in terms of a scalar-valued phase derivative. Through Hardy spaces decomposition we also obtain two forms of uncertainty principles for real-valued signals of finite energy with the first order Sobolev type smoothness.