Hypercyclic operators on algebra of symmetric analytic functions on $\ell_p$ | Zendy

Z. G. Mozhyrovska | Zendy

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Hypercyclic operators on algebra of symmetric analytic functions on $\ell_p$

Author(s) -

Z. G. Mozhyrovska

Publication year - 2016

Publication title -

carpathian mathematical publications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.63

H-Index - 4

eISSN - 2313-0210

pISSN - 2075-9827

DOI - 10.15330/cmp.8.1.127-133

Subject(s) - mathematics , bounded function , automorphism , analytic function , polynomial , operator (biology) , symmetric function , pure mathematics , algebra over a field , combinatorics , discrete mathematics , mathematical analysis , biochemistry , chemistry , repressor , transcription factor , gene

In the paper, it is proposed a method of construction of hypercyclic composition operators on $H(\mathbb{C}^n)$ using polynomial automorphisms of $\mathbb{C}^n$ and symmetric analytic functions on $\ell_p.$ In particular, we show that an "symmetric translation" operator is hypercyclic on a Frechet algebra of symmetric entire functions on $\ell_p$ which are bounded on bounded subsets.

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