Sharp higher-order uncertainty principles
Abstract
We establish a class of sharp higher-order inequalities related to the uncertainty principle. First, by means of the expanding the squares method, we give a concise proof of sharp higher-order Heisenberg uncertainty principles. We provide explicit expressions for the optimal constants and establish the existence of extremal functions. Furthermore, we obtain sharp higher-order Heisenberg uncertainty principles for curl-free vector fields. In particular, when N=2, we give an answer to the higher-order version of Open Problem 9 raised by Maz'ya in [Integr. Equ. Oper. Theory (2018) 90:25]. Second, we establish sharp higher-order Heisenberg uncertainty principles that do not involve higher-order tensors. We also prove sharp higher-order Heisenberg uncertainty principles and higher-order hydrogen uncertainty principles for radially symmetric functions.
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BibTeX
@misc{hu2026sharp,
title = {{Sharp higher-order uncertainty principles}},
author = {Hongtao Hu and Meiqi Liu and Wenming Zou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01561},
eprint = {2610.01561},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01561},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sharp higher-order uncertainty principles
AU - Hongtao Hu
AU - Meiqi Liu
AU - Wenming Zou
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01561
UR - https://arxiv.org/abs/2610.01561
AB - We establish a class of sharp higher-order inequalities related to the uncertainty principle. First, by means of the expanding the squares method, we give a concise proof of sharp higher-order Heisenberg uncertainty principles. We provide explicit expressions for the optimal constants and establish the existence of extremal functions. Furthermore, we obtain sharp higher-order Heisenberg uncertainty principles for curl-free vector fields. In particular, when N=2, we give an answer to the higher-order version of Open Problem 9 raised by Maz'ya in [Integr. Equ. Oper. Theory (2018) 90:25]. Second, we establish sharp higher-order Heisenberg uncertainty principles that do not involve higher-order tensors. We also prove sharp higher-order Heisenberg uncertainty principles and higher-order hydrogen uncertainty principles for radially symmetric functions.
ER -