In this paper, we give a complete characterization of singly generated invariant subspaces in the Hardy space on the unit ball. Then we construct a singly generated invariant subspace that cannot be generated by a single inner function, contrary to the one-variable case where every invariant subspace is generated by a single inner function. Some important properties of invariant subspaces are also determined for singly generated invariant subspaces.
KOCA, BEYAZ BAŞAK and SADIK, NAZIM
"Singly generated invariant subspaces in the Hardy space on the unit ball,"
Turkish Journal of Mathematics: Vol. 43:
2, Article 14.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss2/14