Fock空间中的圆填充与插值
Circle packing and interpolation in Fock spaces
摘要：
James Tung在2005年证明，如果复平面上的点序列$Z=\{z_n\}$满足$$\inf_{n\not=m}|z_n-z_m|>2/\sqrtα,$$，则$Z$是Fock空间$F^p_α$的插值序列。利用圆填充的结果，我们证明了上述常数可以改进为严格小于$2/\sqrtα$的$$\sqrt{2π/(\sqrt3\,α)},$$。对于采样序列也将得到类似的结果。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
