  Let a sequence $\Lambda\subset\mathbb{C}$ be such that the corresponding
system of exponential functions $\mathcal{E}(\Lambda):=\{e^{i\lambda
t}\}_{\lambda\in\Lambda}$ is complete and minimal in $L^2(-\pi,\pi)$ and thus
each function $f\in L^2(-\pi,\pi)$ corresponds to a non-harmonic Fourier series
in $\mathcal{E}(\Lambda)$. We prove that if the generating function $G$ of
$\Lambda$ satisfies Muckenhoupt $(A_2)$ condition on $\mathbb{R}$, then this
series admits a linear summation method. Recent results show that $(A_2)$
condition cannot be omitted.
