I can't say, I looked at this briefly and was hoping for an elementary proof. This paper casts the problem in terms of linear operators over holomorphic functio

I can't say, I looked at this briefly and was hoping for an elementary proof. This paper casts the problem in terms of linear operators over holomorphic function spaces and assumes a number of prior results in that area, and it's been far too long since I read complex analysis. In some sense it's a little unsatisfying that a simple proof has not been found, but this is what makes math so addicting I suppose.