Approximation by Sums of the Form Σk λkh(λkz) in the Disk

Abstract

Given a function h analytic in the unit disk D, we study the density in the space A(D) of functions analytic inside D of the set S(h,E) of sums of the form Σ_k λ_kh(λ_kz) with parameters λ_k ∈ E, where E is a compact subset of \(D\). It is proved, in particular, that if the compact set E “surrounds” the point 0 and all Taylor coefficients of the function h are nonzero, then S(h,E) is dense in A(D).