Wold-type decomposition for Doubly commuting two-isometries

Published 21 Mar 2025 in math.FA | (2503.16933v1)

Abstract: In this article, we prove that any pair of doubly commuting $2$-isometries on a Hilbert space has a Wold-type decomposition. Moreover, the analytic part of the pair is unitary equivalent to the pair of multiplication by coordinate function on a Dirichlet-type space on the bidisc.

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