We give a generalization of the Beurling–Lax theorem both in the complex and quaternionic settings. We consider in the first case functions meromorphic in the right complex half-plane, and functions slice hypermeromorphic in the right quaternionic half-space in the second case. In both settings we also discuss a unified framework, which includes both the disk and the half-plane for the complex case and the open unit ball and the half-space in the quaternionic setting.
Alpay, D., Sabadini, I., 2017. Beurling–Lax type theorems in the complex and quaternionic setting. Linear Algebra and its Applications 530, 15–46. doi:10.1016/j.laa.2017.04.037
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