A description of certain absolutely representing systems (Q1078717)

Let \(A_ R\) be the space of all analytic functions in \(\{\) \(z: | z| \leq R\}\) with an open-compact topology and let f(z) be an entire function. The author proves a criterion for \(\{f(\lambda_ kz)\}^{\infty}_{k=1}\) to be an absolutely representing system in \(A_ R\). The latter means that every \(\phi (z)\in A_ R\) may be represented by an absolutely convergent series \(\phi (z)=\sum_{k\geq 1}c_ kf(\lambda_ kz)\).