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 $$\inf_{n\not=m}|z_n-z_m|>2/\sqrt\alpha,$$ then $Z$ is a sequence of interpolation for the Fock space $F^p_\alpha$. Using results from circle packing, we show that the constant above can be improved to $$\sqrt{2\pi/(\sqrt3\,\alpha)},$$ which is strictly smaller than $2/\sqrt\alpha$. A similar result will also be obtained for sampling sequences.