Circle packing and interpolation in Fock spaces

It was shown by James Tung in 2005 that if a sequence $Z=\{z_n\}$ of points in the complex plane satisfies $\inf_{n\not=m}|z_n-z_m|>2/\sqrtα,$ then $Z$ is a sequence of interpolation for the Fock space $F^p_α$. Using results from circle packing, we show that the constant above can be improved to $\sqrt{2π/(\sqrt3\,α)},$ which is strictly smaller than $2/\sqrtα$. A similar result will also be obtained for sampling sequences.

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