Representation of functions by series of exponents in normed subspaces of $A^\infty(D)$

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 exponents converging in a weakened norm. The main tool in the construction of systems of exponents 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.