Invariant subspaces of the generalized backward shift operator and rational functions

The paper is devoted to a complete characterization of proper closed invariant subspaces the generalized backward shift operator (Pommiez operator) in Fréchet space all holomorphic functions simply connected domain Ω ∋ 0 \Omega \ni 0 complex plane. In case when function that generates this does not have zeros Omega"> encoding="application/x-tex">\Omega , such are finite-dimensional. If addition coincides with entire plane, then under consideration unicellular. has above family splits into two classes: first consists finite-dimensional subspaces, and second infinite-dimensional ones.