Abstract In the paper, we prove theorems in short intervals on approximation of analytic functions by shifts ζ (s + ikh, α), h > 0, k ∈ N 0 k N₀, of the Hurwitz zeta-function. Two cases are discussed. In the first case, it is assumed that the set (log (m + α): m ∈ N 0), 2 π / h \ ( (m+) \,: \, m {N₀), 2 /h\} is linearly independent over Q Q, and it is obtained that the set of the above shifts approximating every analytic function defined on the strip D = s ∈ C: 1 / 2 σ 1 D=\s C\,: \, 1/2 F h, α {F₇, of analytic functions defined on D D such that, for every f ∈ F h, α
Laurinčikas et al. (Mon,) studied this question.