Hardy's uncertainty principle and the Wigner transform from the point of view of symplectic capacities
2009-09-18 14:30 2009-09-18 15:30 2009-09-18 14:30 .. 15:30
by Maurice de Gosson (Faculty of Mathematics, University of Vienna, Austria)
We begin by presenting and discussing the "principle of the symplectic camel", alias Gromov's non-squeezing theorem. This theorem allows the definition of the notion of symplectic capacity, which is beginning to play a crucial role in topological formulations of the uncertainty principle. We restate Hardy's uncertainty principle for the Wigner distribution in terms of this notion, and we make some conjectures.