Agrawal, O. P.; Clark, D. N.; Douglas, R. G. Invariant subspaces in the polydisk. (English) Zbl 0609.47012 Pac. J. Math. 121, 1-11 (1986). From the introduction: ”(The) explicit characterization [due to A. Beurling, Acta Math. 81, 225-238 (1949; Zbl 0034.213)] of the invariant subspaces of the unilateral shift, in terms of the inner-outer factorization has had a major impact.” ”(But) most results (on the corresponding problem for \(H^ 2\) of the polydisk) have gone unpublished, and many results are counterexamples.” ”In this note, we eschew the goal and instead investigate equivalence of invariant subspaces, under joint unitary equivalence. Put another way, we shall consider the problem of characterizing the submodules of the Hardy space over the polydisk algebra.” ”We believe that this may be a worthwhile approach to this problem.” Reviewer: Y.Kato Cited in 1 ReviewCited in 34 Documents MSC: 47A15 Invariant subspaces of linear operators 46E20 Hilbert spaces of continuous, differentiable or analytic functions 42B30 \(H^p\)-spaces 46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces Keywords:invariant subspaces of the unilateral shift; inner-outer factorization; equivalence of invariant subspaces, under joint unitary equivalence; submodules of the Hardy space over the polydisk algebra Citations:Zbl 0034.213 PDFBibTeX XMLCite \textit{O. P. Agrawal} et al., Pac. J. Math. 121, 1--11 (1986; Zbl 0609.47012) Full Text: DOI