Mathematical analysis reveals sharp Heisenberg Uncertainty Principle constants and extremal functions on orthants, establishing rigorous stability estimates for bounded geometric domains.
Though the sharp Heisenberg Uncertainty Principle has been extensively studied in the entire Euclidean spaces, the counterpart on the half spaces or more general orthants has been missing in the literature. We investigate the sharp Heisenberg Uncertainty Principle on orthants by computing explicitly the optimal constant and determining all possible extremal functions. Moreover, we establish several stability estimates of the Heisenberg Uncertainty Principle on the half spaces and orthants.
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Lâm et al. (2026) studied this question.
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