#  Quantum Fourier Analysis 

 



       ![String Fourier Transform (1)](/sites/g/files/omnuum6611/files/styles/hwp_21_9__1920x825/public/mathpicture/files/sft.png?h=f2fd2bb1&itok=tk6J8v5u) 

 

 



 

 



Zhengwei Liu, Sebastian Palcaux, and Jinsong Wu, Fusion Bialgebras and Fourier Analysis, [arXiv:1910.12059](https://arxiv.org/abs/1910.12059).

Chunlan Jiang, Zhengwei Liu, and Jinsong Wu, Block maps and Fourier analysis. Feb 2018, Science China Mathematics, [arxiv:1706.03551](https://arxiv.org/abs/1706.03551).

Zhengwei Liu and Jinsong Wu, Extremal Pairs of Young’s Inequality for Kac Algebras, [*Pacific Journal of Mathematics* 295 (2018), 103–121](https://msp.org/pjm/2018/295-1/p06.xhtml).

Jinsong Wu, Quantum Fourier Analysis *(Talk),* [*International Workshop on Operator Theory and Applications* (2018](/file_url/699)).

Zhengwei Liu and Jinsong Wu, Antisymmetric Characters and Fourier Duality, [arXiv:1805.04783](https://arxiv.org/abs/1805.04783).

Arthur Jaffe and Zhengwei Liu, A Mathematical Picture Language Program, [*Proceedings of the National Academy of Sciences*](http://www.pnas.org/content/early/2017/12/18/1710707114.full.pdf) [115 (2018), 81–86](http://www.pnas.org/content/early/2017/12/18/1710707114.full.pdf).

Arthur Jaffe, Zhengwei Liu, and Alex Wozniakowski, Holographic Software for Quantum Networks, [*Science China Mathematics* 61 (2018), 593–626](https://link.springer.com/article/10.1007/s11425-017-9207-3).

Zhengwei Liu, Simeng Wang, and Jinsong Wu, Young’s inequality for locally compact quantum groups, *Journal of Operator Theory* [77 (2017), 109](http://dx.doi.org/10.7900/jot.2016mar03.2104)[–](https://scholar.harvard.edu/files/liu/files/the_noncommutative_fourier_transform.pdf)[131](http://dx.doi.org/10.7900/jot.2016mar03.2104)*.*

Chunlan Jiang, Zhengwei Liu, and Jinsong Wu, Uncertainty principles for locally compact quantum groups, [*Journal of Functional Analysis* 274 (2017) 2399-2445](https://www.sciencedirect.com/science/article/pii/S0022123617303580).

Zhengwei Liu and Jinsong Wu, The Noncommutative Fourier Transform: A survey, [*Acta Mathematica Sinica Chinese Series* (In honor of the 75th birthday of Bingren Li) 60 (2017), 69–80](https://scholar.harvard.edu/files/liu/files/the_noncommutative_fourier_transform.pdf).

Zhengwei Liu and Jinsong Wu, Uncertainty principle for Kac algebras, [*Journal of Mathematical Physics*](http:/dx.doi.org/10.1063/1.4983755) [58](http://dx.doi.org/10.1063/1.4983755) [(2017), 052102.](http://dx.doi.org/10.1063/1.4983755)

Arthur Jaffe and Zhengwei Liu, Planar Para Algebras, Reflection Positivity, [*Communications in Mathematical Physics* 352 (2017), 95–133](http://dx.doi.org/10.1007/s00220-016-2779-4).

Zhengwei Liu, Quon Language: Surface Algebras and Fourier Duality, [arXiv:1707.03995](https://arxiv.org/abs/1707.03995), [*Communications in Mathematical Physics* 366 (2019), 865–894](https://link.springer.com/article/10.1007/s00220-019-03361-3).

Chunlan Jiang, Zhengwei Liu, and Jinsong Wu, Noncommutative uncertainty principles, [arXiv:1408.1165](https://arxiv.org/abs/1408.1165), [*Journal of Functional Analysis* 270 (2016), 264–311](http://www.sciencedirect.com/science/article/pii/S0022123615003237).

Zhengwei Liu, Exchange relation planar algebras of small rank, [arXiv:1308.5656](https://arxiv.org/abs/1308.5656), [*Transactions of the American Mathematical Society* 368 (2016), 8303-8348](https://www.ams.org/tran/2016-368-12/S0002-9947-2016-06582-4/).