Wold decomposition for doubly commuting isometries

In this paper, we obtain a complete description of the class of n  -tuples (n⩾2n⩾2) of doubly commuting isometries. In particular, we present a several variables analogue of the Wold decomposition for isometries on Hilbert spaces. Our main result is a generalization of M. Slocinskiʼs Wold-type decomposition of a pair of doubly commuting isometries.