An Uncertainty Principle for Operators

Abstract

Hardy—s Uncertainty Principle asserts that if f is a function on ℝⁿ such that exp(α | · |²)f and exp$(\beta | \cdot |^2 )\hat f$ are bounded, where $\alpha \beta > \tfrac{1} {4}$, then f = 0. In this paper, we prove a version of Hardy—s result for operators.

This paper was prepared at the University of New South Wales. The second-named author was supported by an ARC grant held by the first-named author. She wishes to express her thanks for this support.