Isomorphism of spaces of analytic functions on $n$-circular domains

Abstract

The space $A(D) $ of all analytic functions in a complete $n$ -circular domain $D$ in $\mathbb{C}^{n},$ $n\geq 2,$ is considered with a natural Fréchet topology. Some sufficient conditions for the isomorphism of such spaces are obtained in terms of certain subtle geometric characteristic of domains $D$. This investigation complements essentially the second author's result on necessary geometric conditions of such isomorphisms.