Interpolating and sampling sequences for entire functions
Abstract
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 & OrtegaCerdà and OrtegaCerdà & Seip for the case when the Laplacian of phi is bounded above and below.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2002
 DOI:
 10.48550/arXiv.math/0205241
 arXiv:
 arXiv:math/0205241
 Bibcode:
 2002math......5241M
 Keywords:

 Mathematics  Complex Variables;
 30E05;
 46E20
 EPrint:
 Geom. Funct. Anal. 13 (2003), no. 4, 862914.