Representation of Functions by Series of Exponentials in Normed Subspaces of A∞(D)

We introduce the normalized space of functions that are analytic in a bounded convex domain and infinitely differentiable up to its boundary, with estimates of all derivatives determined by a logarithmically convex sequence of positive numbers. We prove that functions from this space are represented by series of exponentials converging in a weakened norm. The main tool in the construction of systems of exponentials are entire functions with a given asymptotic behavior. Also, a theorem on the joint approximation of subharmonic functions by the logarithms of the modules of entire functions is proved.