Isomorphism of spaces of analytic functions on \(n\)-circular domains (Q2469062)

Continuing classical work by Aizenberg, Mityagin, Rolewicz and Zahariuta, the authors investigate the isomorphic classification of Fréchet spaces \(A(D)\) of analytic functions on a complete \(n\)-circular (Reinhardt) domain \(D\) in \(\mathbb{C}^n, n \geq 2\). Zahariuta obtained in 1977 a necessary condition for the isomorphism of spaces \(A(D)\) in terms of a geometric characteristic of the domains. Some sufficient conditions for the isomorphism in terms of the same characteristics are presented now. These results are obtained as a consequence of a more general theorem about the isomorphic classification of certain types of Köthe sequence spaces.