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A new analytic model for left-invertible operators is introduced andinvestigated. We show that left-invertible operator $T$, which satisfiescertain conditions can be modelled as a multiplication operator $\mathscr{M}_z$on a reproducing kernel Hilbert space of vector-valued analytic functions on anannulus or a disc. A similar result for composition operators in$\ell^2$-spaces is established.

A Shimorin-type analytic model for left-invertible operators on an annulus and applications