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 (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.