Complex Methods

The complex point of view opens wide prospects for our theme: in its different manifestations the uncertainty principle arises as a corollary of the various uniqueness theorems in which complex analysis is so rich. Here is a crude example: the fact that any charge μ εM (ℝ) with bounded support and bounded spectrum vanishes identically follows immediately from the fact that µ coincides on ℝ with some entire function if diam supp µ < +∞. It is clear that this primitive consideration can be developed into much more precise results.