Akhiezer's theorem
In the mathematical field of complex analysis, Akhiezer's theorem is a result about entire functions proved by Naum Akhiezer.
Let f(z) be an entire function of exponential type τ, with f(x) ≥ 0 for real x. Then the following are equivalent:
where zn are the zeros of f.
It is not hard to show that the Fejér–Riesz theorem is a special case.
...
Wikipedia