The fundamental principle for invariant subspaces

The problem of a fundamental principle for subspaces invariant under the operator of differentiation for subspaces of functions analytic in a limited convex domain of a complex plane admitting spectral synthesis. This problem has already been solved earlier with one restriction on multiplicity of eigenvalues of differentiation operators. This restriction is removed in the present paper. Thus, we give a complete solution of a fundamental principle problem for arbitrary non-trivial closed invariant subspaces, admitting a spectral synthesis in arbitrary limited convex domains.