Singly generated invariant subspaces in the Hardy space on the unit ball

Authors: BEYAZ BAŞAK KOCA, NAZIM SADIK

Abstract: 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.

Keywords: Invariant subspace, Hardy space, ball, inner function, factorization

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