Countably Generated Algebras of Analytic Functions on Banach Spaces

In the paper, we study various countably generated algebras of entire analytic functions on complex Banach spaces and their homomorphisms. Countably often appear as symmetric with respect to a group symmetries, are interesting for possible applications. Some conditions existence topological isomorphisms between such obtained. We construct class algebras, where all normalized algebraic bases equivalent. On other hand, find non-isomorphic classes algebras. addition, establish hypercyclicity derivations in bounded type. use methods from theory several variables, commutative Fréchet linear dynamical systems.