Show that if $f ( x ) = 0$ for all $x \in \mathbf { R } _ { + }$ then $a _ { n } = 0$ for all $n \in \mathbf { N }$. Here $f = \sum_{n\geq 0} a_n e^{-\lambda_n x}$ is the sum of a Dirichlet series.
Show that if $f ( x ) = 0$ for all $x \in \mathbf { R } _ { + }$ then $a _ { n } = 0$ for all $n \in \mathbf { N }$.
Here $f = \sum_{n\geq 0} a_n e^{-\lambda_n x}$ is the sum of a Dirichlet series.