Subspaces of analytic functions that are invariant with respect to the multiple-differentiation operator (Q1091566)

The problem of completeness of exponential polynomials in subspaces of analytic functions invariant with respect to the operator of multiple differentiation is transferred to the similar problem for the operator of componentwise differentiation in some spaces of vector-valued functions. The author constructs some examples which give the negative answer to some questions about spectral theory of ordinary differential operators in complex domain formulated by \textit{V. A. Tkachenko} in the volume ''99 unsolved problems of linear and complex analysis'', LOMI, 1978 (see problem 6.5).