Multiple sampling and interpolation in a space of polynomials
Complex Variables
2026-02-09 v1
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.
Cite
@article{arxiv.2405.19945,
title = {Multiple sampling and interpolation in a space of polynomials},
author = {Carlos A. Cruz and Xavier Massaneda and Joaquim Ortega-Cerdà},
journal= {arXiv preprint arXiv:2405.19945},
year = {2026}
}