Cross Theorems for Separately $(\cdot, W)$-meromorphic Functions

Abstract

It is shown that Rothstein's theorem holds for $(F, W)$-meromorphic functions with $F$ is a sequentially complete locally convex space. We also prove that a meromorphic function on a Riemann domain $D$ over a separable Banach $E$ with values in a sequentially complete locally convex space can be extended meromorphically to the envelope of holomorphy $\widehat{D}$ of $D$. Using these results, in the remaining parts, we give a version of Kazarian's theorem for the class of separately $(\cdot, W)$-meromorphic functions with values in a sequentially complete locally convex space and generalize cross theorem with pluripolar singularities of Jarnicki and Pflug for separately $(\cdot, W)$-meromorphic functions with values in a Fréchet space.