Noncommutative uncertainty principles

Chunlan Jiang Zhengwei Liu Jinsong Wu

Spectral Theory and Operator Algebra mathscidoc:1912.431046

Journal of Functional Analysis, 270, (1), 264-311, 2016.1
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 HausdorffYoung inequality, Young's inequality, the HirschmanBeckner uncertainty principle, the DonohoStark 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 <i></i>-lattices, modular tensor categories, etc.
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  title={Noncommutative uncertainty principles},
  author={Chunlan Jiang, Zhengwei Liu, and Jinsong Wu},
  booktitle={Journal of Functional Analysis},
Chunlan Jiang, Zhengwei Liu, and Jinsong Wu. Noncommutative uncertainty principles. 2016. Vol. 270. In Journal of Functional Analysis. pp.264-311.
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