Geometric conditions for interpolation in weighted spaces of entire functions

Details Geometric conditions for interpolation in weighted spaces of entire functions Geometric conditions for interpolation in weighted spaces of entire functions

2006-05-30

arxiv.org/abs/math/0605760v3

J. Geom. Anal. 17 (2007), no.8, 701-716

Mathematics

Complex Variables

Scientific paper

We use $L^2$ estimates for the $\bar\partial$ equation to find geometric
conditions on discrete interpolating varieties for weighted spaces $A_p(\C)$ of
entire functions such that $| f(z)|\le Ae^{Bp(z)}$ for some $A,B>0$. In
particular, we give a characterization when $p(z)=e^{| z|}$ and more generally
when $\ln p(e^r)$ is convex and $\ln p(r)$ is concave.

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