Some finite-dimensional backward-shift-invariant subspaces in the ball and a related interpolation problem

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We solve Gleason's problem in the reproducing kernel Hilbert space with repoducing kernel\(1/\left( {1 - \sum\nolimits_1^N {z_j w_j^* } } \right)\). We define and study some finite-dimensional resolvent-invariant subspaces that generalize the finite-dimensional de Branges-Rovnyak spaces to the setting of the ball.