Composition Operators on Hilbert Spaces of Entire Functions of Several Variables

2017 ◽  
Vol 88 (3) ◽  
pp. 301-330
Author(s):  
Minh Luan Doan ◽  
Le Hai Khoi ◽  
Trieu Le
Keyword(s):  
Hilbert Spaces ◽  
Entire Functions ◽  
Composition Operators ◽  
Several Variables

Composition operators on Hilbert spaces of entire functions

2017 ◽  
Vol 61 (10) ◽  
pp. 1-4
Author(s):  
A. V. Abanin ◽  
T. I. Abanina
Keyword(s):  
Hilbert Spaces ◽  
Entire Functions ◽  
Composition Operators

scholarly journals Composition operators on Hilbert spaces of entire functions

2015 ◽  
Vol 353 (6) ◽  
pp. 495-499 ◽  
Author(s):  
Minh Luan Doan ◽  
Le Hai Khoi
Keyword(s):  
Hilbert Spaces ◽  
Entire Functions ◽  
Composition Operators

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

2016 ◽  
Vol 8 (1) ◽  
pp. 127-133 ◽  
Author(s):  
Z.G. Mozhyrovska
Keyword(s):  
Analytic Functions ◽  
Entire Functions ◽  
Composition Operators ◽  
Translation Operator ◽  
Hypercyclic Operators ◽  
Polynomial Automorphisms ◽  
Fréchet Algebra

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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