On a Beurling-Arveson type theorem for some functional Hilbert spaces and related questions (Q733612)

This is a contribution to the investigation of invariant subspaces of the unilateral shift \(Sf(z)=zf(z)\) which was started, for the Hardy space on the unit disc, by the well-known Beurling theorem [\textit{A. Beurling}, Acta Math., Uppsala 81, 239--255 (1949; Zbl 0033.37701)]. Here, a Beurling-Arveson type theorem for some more general Hilbert spaces of complex-valued functions on the unit disk is proved. The author also answers a question of \textit{R.-W. Yang} [Integral Equations Oper. Theory 48, No. 3, 411--423 (2004; Zbl 1061.46023)] concerning the Hardy space on bi-disc.