A uniqueness theorem for entire functions

A. G. Ramm

Let $G(k)={\int }_0^{1}g(x)e^{kx}dx$, $g\in L^1(0,1)$. The main result of this paper is the following theorem. {\bf Theorem}. {\it If ${\mathrm{limsup}}_{k\to +\infty }|G(k)|<\infty$, then $g=0$.…