The classical Mittag-Leffler theorem on meromorphic functions is extended to the case of functions and hyperfunctions belonging to the kernels of linear partial differential operators with constant coefficients.
The paper is devoted to infinitely differentiable one-parameter convolution semigroups in the convolution algebra of matrix valued rapidly decreasing distributions on ℝⁿ. It is proved that is the generating distribution of an i.d.c.s. if and only if the operator on satisfies the Petrovskiĭ condition for forward evolution. Some consequences are discussed.