Circle packing and interpolation in Fock spaces

Abstract

It was shown by James Tung in 2005 that if a sequence $Z=\{z_n\}$ of points in the complex plane satisfies $$\underset{n\ne m}{\inf }|z_n-z_m|>2/\sqrt{\alpha },$$ then $Z$ is a sequence of interpolation for the Fock space $F_{\alpha }^p$. Using results from circle packing, we show that the constant above can be improved to $$\sqrt{2\pi /(\sqrt{3}\alpha )},$$ which is strictly smaller than $2/\sqrt{\alpha }$. A similar result will also be obtained for sampling sequences.

7 pages