Open AccessHypercyclic operators on algebra of symmetric analytic functions on $\ell_p$
Author(s) -
Z. G. Mozhyrovska
Publication year - 2016
Publication title -
karpatsʹkì matematičnì publìkacìï
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 , translation (biology) , pure mathematics , algebra over a field , combinatorics , discrete mathematics , mathematical analysis , biochemistry , chemistry , repressor , messenger rna , 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.