Every inner function on the n-dimensional polydisc is, up to unitaries and a constant direct summand, the characteristic function of a Beurling tuple of commuting contractions, defined by an explicit operator formula.
Athavale, On joint hyponormality of operators , Proc
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Inner and characteristic functions in polydiscs
Every inner function on the n-dimensional polydisc is, up to unitaries and a constant direct summand, the characteristic function of a Beurling tuple of commuting contractions, defined by an explicit operator formula.