The Müntz–Szasz problem

A condition is obtained on the placement of point $\lambda_n$ (in some sense, the final point) with which completeness of the system of functions $\{\exp(-\lambda_nx)\}$, $\operatorname{Re}\lambda_n>0$, in spaces $L^p$, $1\le p<2$. is equivalent to divergence of the series $\sum\operatorname{Re}\lambda_n(1+|\lambda_n|^2)^{-1}$.