Phase retrieval in infinite-dimensional Hilbert spaces
  The main result of this paper states that phase retrieval in infinite-dimensional Hilbert spaces is never uniformly stable, in sharp contrast to the finite dimensional setting in which phase retrieval is always stable. This leads us to derive stability results for signals depending on how well they are approximated by finite expansions. 
Jameson Cahill, Peter G. Casazza, Ingrid Daubechies
math.FA