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Interpolating and sampling sequences for entire functions. (English) Zbl 1097.30041
Summary: We characterise interpolating and sampling sequences for the spaces of entire functions $f$ such that $fe^{-\phi}\in L^p(\Bbb C)$, $p\geq1$, where $\phi$ is a subharmonic weight whose Laplacian is a doubling measure. The results are expressed in terms of some densities adapted to the metric induced by $\Delta\phi$. They generalise previous results by Seip for the case $\phi(z) = \vert z\vert^2$, Berndtsson and Ortega-Cerdà and Ortega-Cerdà and Seip for the case when $\Delta\phi$ is bounded above and below, and Lyubarskij and Seip for 1-homogeneous weights of the form $\phi(z) = \vert z\vert h(\text{arg}z)$, where $h$ is a trigonometrically strictly convex function.

MSC:
30D60Quasi-analytic and other classes of complex functions in one variable
60H05Stochastic integrals
46E15Banach spaces of continuous, differentiable or analytic functions
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