On the completeness of sparse subsequences of systems of functions of the form $f^{(n)}(\lambda_nz)$

We obtain some new results on the completeness of systems of functions $f^{(n)}(\lambda_nz)$ in the space of entire functions with the topology of uniform convergence on an arbitrary compact set in $\mathbb C$. In the presence of lacunae in the Taylor expansion of the function $f(z)$, we prove the existence of bases consisting of subsystems of this form.