Let $\omega \subseteq {\bb R}^d$ be an open domain. The sequentially complete DF-spaces $E$ are characterized such that for each (some) discrete sequence $(z_n) \subseteq \omega$ , a sequence of natural numbers $(k_n)$ and any family $(x_{n, \alpha})_{n \in {\bb N}, \vert \alpha\vert \leqslant k_n} \subseteq E$ the infinite system of equations \[ \left(\frac{\partial^{\vert \alpha\vert } f}{\partial z^{\alpha}}\right)(z_n) = x_{n,\alpha} \quad \hbox{for } n \in {\bb N}, \alpha \in {\bb N}^{d}, \vert \alpha\vert \leqslant k_n, \] has an $E$ -valued real analytic solution $f$ .