Invariant subspaces and unicellularity of operators of generalized integration in spaces of analytic functionals

Invariant subspaces are described and the unicellularity is proved of one class of operators of generalized integration in spaces of analytic functionals. As one of the realizations it is established that every nontrivial subspace, invariant relative to the integration $\int_a^zF(t)\,dt$, in the space of functions analytic in an arbitrary convex domain $\Omega$ ($a\in\Omega$), is determined by a positive integer m and consists of all functions equal to zero at point $a$ together with all derivatives up to order $m-1$.