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The space A(D) of all analytic functions in a complete n-circular do- main D in Cn; n 2; is considered with a natural Frechet topology. Some su¢ cient conditions for the isomorphism of such spaces are ob- tained in terms of certain subtle geometric characteristic of domains D. This investigation complements essentially the second authors result [8] on necessary geometric conditions of such isomorphisms.

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