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Rudin, Walter

doi:10.1512/iumj.1982.31.31050

Cited by 31 publications

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“…Then, y 0 = 1 and Q(y 0 ) = 0. But, this contradicts the property of proper maps in [74], mentioned above, suggesting that Q −1 n (0) = 0.…”

Section: Derivations In Countable Generated Algebrasmentioning

confidence: 84%

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Countably Generated Algebras of Analytic Functions on Banach Spaces

Novosad,

Vasylyshyn,

Zagorodnyuk

2023

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

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“…Then, y 0 = 1 and Q(y 0 ) = 0. But, this contradicts the property of proper maps in [74], mentioned above, suggesting that Q −1 n (0) = 0.…”

Section: Derivations In Countable Generated Algebrasmentioning

confidence: 84%

“…It is known (see, e.g., [73], Chapter 15) that a proper map is surjective and open. In [74], it is proved that if polynomials Q 1 , . .…”

Section: Derivations In Countable Generated Algebrasmentioning

confidence: 99%