# A. Yu. Popov, On the completeness of sparse subsequences of systems of functions of the form $f^{(n)} ({\lambda}_n z)$

Title: On the completeness of sparse subsequences of systems of functions of the form $f^{(n)} ({\lambda}_n z)$
Authors: A. Yu. Popov
Journal title: Izvestiya: Mathematics
Year: 2004
Issue: 5
Volume: 68
Pages: 1025–1049
Citation:

A. Yu. Popov, “On the completeness of sparse subsequences of systems of functions of the form $f^{(n)} ({\lambda}_n z)$”, Izvestiya: Mathematics, 2004, 68:5, 1025–1049

Abstract:

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