Criterion of fundamental principle

Abstract

In the work we study the subspace of functions analytic in a convex domain and invariant with respect to the differentiation operator. We study the fundamental principle problem, namely, on representation of all functions in the invariant subspace by the series of exponential monomials. These exponential monomials are the eigenfunctions and generalized eigenfunctions of differentiation operator in the invariant subspace. We obtain a simple geometric criterion of fundamental principle. We also obtain a similar criterion for solvability of an interpolation problem in the spaces of entire functions of exponential type.