On approximating two distributions from a single complex-valued function
  We consider the problem of approximating two, possibly unrelated probability distributions from a single complex-valued function $\psi$ and its Fourier transform. We show that this problem always has a solution within a specified degree of accuracy, provided the distributions satisfy the necessary regularity conditions. We describe the algorithm and construction of $\psi$ and provide examples of approximating several pairs of distributions using the algorithm. 
W.D. Flanders and G. Japaridze
math-ph math.MP