The regularity of the space of germs of Fréchet valued holomorphic functions and the mixed Hartog's theorem - Quang, Thai Thuan (MATHEMATICA SCANDINAVICA, 2006)
It is shown that $H(K, F)$ is regular for every reflexive Fréchet space $F$ with the property ($LB_∞)$ where $K$ is a compact set of uniqueness in a Fréchet-Schwartz space $E$ such that $E \in (Ω)$. Using this result we give necessary and sufficient conditions for a Fréchet space $F$, under which every separately holomorphic function on $K × F^*$ is holomorphic, where $K$ is as above.