2008
DOI: 10.1007/s11425-007-0184-3
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Beurling’s theorem and invariant subspaces for the shift on Hardy spaces

Abstract: Let G be a bounded open subset in the complex plane and let H 2 (G) denote the Hardy space on G. We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riemann map from W onto the unit disk D is almost 1-1 with respect to the Lebesgue measure on ∂D and if the Riemann map belongs to the weak-star closure of the polynomials in H ∞ (W ). Our main theorem states: in order that for each M ∈ Lat (Mz), there exist u ∈ H ∞ (G) such that M = ∨{uH 2 (G)}, it … Show more

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Cited by 2 publications
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