Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation

The Improvement of the Heisenberg Uncertainty Principle

Convex Functions on the Heisenberg Group

Convex functions in Euclidean space can be characterized as universal viscosity subsolutions of all homogeneous fully nonlinear second order elliptic partial differential equations. This is the starting point we have chosen for a theory of convex functions on the Heisenberg group.

Position measuring interactions and the Heisenberg uncertainty principle

Measurements disturb microscopic objects inevitably. The problem still remains open as to how measurements disturb their objects. It is frequently claimed that if one measures position with noise , the momentum is disturbed at least h̄/2 [1, p. 230]. This claim is often called the Heisenberg uncertainty principle. The Heisenberg principle has been demonstrated typically by a thought experiment u...

The Heisenberg group and Hermite functions

Quantitative Unique Continuation, Logarithmic Convexity of Gaussian Means and Hardy’s Uncertainty Principle

In this paper we describe some recent works on quantitative unique continuation for elliptic, parabolic and dispersive equations. We also discuss recent works on the logarithmic convexity of Gaussian means of solutions to Schrödinger evolutions and the connection with a well-known version of the uncertainty principle, due to Hardy. The elliptic results are joint work with J. Bourgain [BK], whil...