Unbounded Pseudoconvex Domains in $${\mathbb {C}}^n$$ and Their Invariant Metrics

$$L_h^2$$ L h 2 -Functions in Unbounded Balanced Domains

“…Basic objects of study in several complex variables are domains of holomorphy defined as follows. For the family F ⊂ O(D) we say that the domain D ⊂ C n is an F -domain of holomorphy if there are no domains D 0 , D 1 ⊂ C n with ∅ = D 0 ⊂ D 1 ∩ D, D 1 D such that for any f ∈ F there exists anf ∈ O(D 1 ) withf ≡ f on D 0 .…”

“…We think the methods and ideas presented in our paper may help the Reader to develop new methods to cope with the problems. Let us mention here that recently a lot of effort was invested in investigation of these problems in many classes of unbounded domains (see e. g. [2], [3], [4], [1], [15] or [16]). As we saw a problem of Wiegerinck drew a lot of effort recently and except for partial results already mentioned above the problem was repeated in a recent survey on problems in the theory of several complex variables ( [5]).…”