On a linear interpolation problem for nn-dimensional vector polynomials

This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding nn scalar polynomials such that an equation involving a linear combination of them is satisfied for each one of the NN interpolation nodes. The results of this work generalize previous results on the so-called rational interpolation and have applications to direct and inverse spectral analysis of band matrices.