Fresh from the oven:

[A Polynomial Time Algorithm for Lossy Population Recovery][1]
By: Ankur Moitra, Michael Saks

Quoting from the paper: "Here we will prove the uncertainty principle stated in the previous section using tools from complex analysis. Perhaps one of the most useful theorems in understanding the rate of growth of holomorphic functions in the complex plane is Hadamard’s Three Circle Theorem..."

  [1]: http://front.math.ucdavis.edu/1302.1515