Interpolating and sampling sequences for entire functions

Details Interpolating and sampling sequences for entire functions Interpolating and sampling sequences for entire functions

2002-05-23

arxiv.org/abs/math/0205241v1

Geom. Funct. Anal. 13 (2003), no. 4, 862--914.

Mathematics

Complex Variables

Scientific paper

We characterise interpolating and sampling sequences for the spaces of entire functions f such that f e^{-phi} belongs to L^p(C), p>=1 (and some related weighted classes), 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 the Laplacian of phi. They generalise previous results by Seip for the case phi(z)=|z|^2, and by Berndtsson & Ortega-Cerd\`a and Ortega-Cerd\`a & Seip for the case when the Laplacian of phi is bounded above and below.

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