Uncertainty principles for orthonormal bases

Abstract

In this survey, we present various forms of the uncertainty principle (Hardy, Heisenberg, Benedicks). We further give a new interpretation of the uncertainty principles as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro. Finally, we show that Benedicks' result implies that solutions of the Shrödinger equation have some (appearently unnoticed) energy dissipation property.

Cited by in corpus (2)

• Nazarov's uncertainty principles in higher dimension
• Hardy's Uncertainty Principle, Convexity and Schrödinger Evolutions