A uniqueness theorem for entire functions

Details A uniqueness theorem for entire functions A uniqueness theorem for entire functions

2010-01-03

arxiv.org/abs/1001.0367v1

Mathematics

Complex Variables

Scientific paper

Let $G(k)=\int_0^1g(x)e^{kx}dx$, $g\in L^1(0,1)$. The main result of this paper is the following theorem. {\bf Theorem}. {\it If $\limsup_{k\to +\infty}|G(k)|<\infty$, then $g=0$. There exists $g\not\equiv 0$, $g\in L^1(0,1)$, such that $G(k_j)=0$, $k_j0$ is.}

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