Separately analytic functions and generalizations of Hartogs' theorem

Official URL: http://192.168.1.20/record=b1276344 (Table of Contents)

Let D and G be arbitrary Stein manifolds, E ⊂ D and F ⊂ G compact sets, and X = (E X G) ∪ (D X F). Under certain general hypothesis it is proved that a function f on X which is separately analytic, i.e. for which f(z;w) is analytic in z in D for any fixed w ∈ F and analytic in w in G for any fixed z ∈ E, extends to an analytic function in some open neighbourhood ~X of X.