中文摘要：

基于解析平移不变Mercer核的再生核希尔伯特空间，利用再生性，证明当核是解析时，再生核希尔伯特空间中的每一个函数都是实解析的，并且给出了收敛半径．

英文摘要：

Based on reproducing kernel Hilbert spaces （ RKHS ）associated with translation-invariant Mercer kernels, prove that when the kernel is real analytic, every function from the RKHS is real analytic, and gave its radius of convergence by applying a special derivative reproducing property.