Invariant subspaces in unbounded domains

We study subspaces of functions analytic in an unbounded convex domain of the complex plane and invariant with respect to the differentiation operator. This paper is devoted to the study of the problem of representing all functions from an invariant subspace by series of exponential monomials. These exponential monomials are eigenfunctions and associated functions of the differentiation operator in the invariant subspace. A simple geometric criterion of the fundamental principle is obtained. It is formulated just in terms of the Krisvosheev condensation index for the sequence of exponents of the mentioned exponential monomials.