Coefficient multipliers with closed range

Abstract

For two power series and with positive radii of convergence, the Hadamard product or convolution is defined by . We consider the prblem of characterizing those convolution operators acting on spaces of holomorphic functions which have closed range. In particular, we show that every Euler differential operator is a convolution operator and we characterize the Euler differential operators, which are surjective on the space of holomorphic functions on every domain which contains the origin.