Heisenberg Uncertainty Principle on half spaces and Orthants: Best constants, Optimizers and Stability

TL;DR

This paper investigates the sharp Heisenberg Uncertainty Principle on half spaces and orthants, explicitly computes optimal constants, identifies extremal functions, and establishes stability estimates for these geometric domains.

Contribution

It provides the first explicit computation of optimal constants and extremizers for the Heisenberg Uncertainty Principle on orthants, along with stability results.

Findings

Explicit optimal constants for half spaces and orthants.

Characterization of all extremal functions.

Stability estimates for the uncertainty principle.

Abstract

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.