Noncommutative uncertainty principles

详细信息    查看全文

• 作者：Chunlan Jiang^a ; ¹ ; ^{cljiang@mail.hebtu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Zhengwei Liu^b ; ² ; ^{zhengwei.liu@vanderbilt.edu" class="auth_mail" title="E-mail the corresponding author} ; Jinsong Wu^c ; ³ ; ^{wjsl@ustc.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：46L37 ; 43A30 ; 94A15
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：1 January 2016
• 年：2016
• 卷：270
• 期：1
• 页码：264-311
• 全文大小：882 K

文摘

The classical uncertainty principles deal with functions on abelian groups. In this paper, we discuss the uncertainty principles for finite index subfactors which include the cases for finite groups and finite dimensional Kac algebras. We prove the Hausdorff–Young inequality, Young's inequality, the Hirschman–Beckner uncertainty principle, the Donoho–Stark uncertainty principle. We characterize the minimizers of the uncertainty principles and then we prove Hardy's uncertainty principle by using minimizers. We also prove that the minimizer is uniquely determined by the supports of itself and its Fourier transform. The proofs take the advantage of the analytic and the categorial perspectives of subfactor planar algebras. Our method to prove the uncertainty principles also works for more general cases, such as Popa's λ-lattices, modular tensor categories, etc.