Approximation of analytic functions by generalized shifts of the Lerch zeta-function

In the paper, we approximate analytic functions by generalized shifts $L(\lambda, \alpha, s+ig(\tau))$, $s=\sigma+it$, of the Lerch zeta-function, where $g$ is a certain increasing to $+\infty$ real function having a monotonic derivative. We prove that, for arbitrary parameters $\lambda$ and $\alpha$, there exists a closed set $\FF_{\lambda, \alpha}$ of analytic functions defined in the strip $1/2< \sigma<1$ which functions are approximated by the above shifts. If the set of logarithms $\log(m+\alpha)$, $m\in \NN_0$, is linearly independent over the field of rational numbers, then the set $\FF_{\lambda, \alpha}$ coincides with the set of all analytic functions in that strip.