Abstract
This article presents the Heisenberg–Pauli–Weyl uncertainty inequality for the Radon transform on the Heisenberg group, which indicates that the Radon transform and the Fourier transform of a nonzero function can not both be sharply localized. The proof is mainly based on some estimates related to the heat kernel, together with the relation between the sublaplacian and the group Fourier transform.
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Communicated by Sanne ter Horst, Dmitry Kaliuzhnyi-Verbovetskyi and Izchak Lewkowicz.
This work was supported by the National Natural Science Foundation of China (Nos. 11501131, 11271091 and 11471040).
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Xiao, J., He, J. Uncertainty Inequality for Radon Transform on the Heisenberg Group. Complex Anal. Oper. Theory 11, 1603–1612 (2017). https://doi.org/10.1007/s11785-016-0533-8
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DOI: https://doi.org/10.1007/s11785-016-0533-8