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arXiv · 2405.19945

Multiple sampling and interpolation in a space of polynomials

Carlos A. Cruz·Xavier Massaneda·Joaquim Ortega-Cerdà
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Abstract

We study sampling and interpolation arrays with multiplicities for the spaces P_k 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 P_k as k tends to infinity.

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Carlos A. Cruz, Xavier Massaneda, Joaquim Ortega-Cerdà. 2024-05-30. Multiple sampling and interpolation in a space of polynomials. https://doi.org/10.1007/s00041-025-10228-w

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