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We study sampling and interpolation arrays with multiplicities for the spaces Pₖ of holomorphic polynomials of degree at most k. We find that the geometric conditions satisfied by these arrays are in accordance with the conditions satisfied by the sampling and interpolating sequences with unbounded multiplicities in the Fock space, which can be seen as a limiting case of the space Pₖ as k tends to infinity.
Cruz et al. (Thu,) studied this question.