Every doubly twisted near-isometry admits a unique Wold-type decomposition, with explicit summands, unitary equivalence characterization, and an analytic model.
Sarkar,Wold decomposition for doubly commuting isometries, Linear Alge- bra and its Applications445(2014), 289-301
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Doubly twisted near-isometries: Classification and a Wold-type decomposition
Every doubly twisted near-isometry admits a unique Wold-type decomposition, with explicit summands, unitary equivalence characterization, and an analytic model.