Abstract
We introduce block maps for subfactors and study their dynamic systems. We prove that the limit points of the dynamic system are positive multiples of biprojections and zero. For the ℤ2 case, the asymptotic phenomenon of the block map coincides with that of the 2D Ising model. The study of block maps requires a further development of our recent work on the Fourier analysis of subfactors. We generalize the notion of sum set estimates in additive combinatorics for subfactors and prove the exact inverse sum set theorem. Using this new method, we characterize the extremal pairs of Young’s inequality for subfactors, as well as the extremal operators of the Hausdorff-Young inequality.
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Acknowledgements
Chunlan Jiang was supported by National Natural Science Foundation of China (Grant No. A010602) and National Excellent Doctoral Dissertation of China (Grant No. 201116). Zhengwei Liu was supported by the Templeton Religion Trust (Grant Nos. TRT0080 and TRT0159) and an AMS-Simons Travel Grant. Jinsong Wu was supported by National Natural Science Foundation of China (Grant Nos. 11771413 and 11401554). Zhengwei Liu thanks Vaughan Jones for constant encouragement and Terence Tao for helpful suggestions. Parts of the work was done during visits of Zhengwei Liu and Jinsong Wu to Hebei Normal University.
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Jiang, C., Liu, Z. & Wu, J. Block maps and Fourier analysis. Sci. China Math. 62, 1585–1614 (2019). https://doi.org/10.1007/s11425-017-9263-7
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DOI: https://doi.org/10.1007/s11425-017-9263-7