Polynomial automorphisms and hypercyclic operators on spaces of analytic functions

2007 ◽  
Vol 89 (2) ◽  
pp. 157-166 ◽  
Author(s):  
Zoryana Novosad ◽  
Andriy Zagorodnyuk
Keyword(s):  
Analytic Functions ◽  
Hypercyclic Operators ◽  
Polynomial Automorphisms ◽  
Spaces Of Analytic Functions

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.

scholarly journals Integration Operators in Average Radial Integrability Spaces of Analytic Functions

2021 ◽  
Vol 18 (3) ◽  
Author(s):  
Tanausú Aguilar-Hernández ◽  
Manuel D. Contreras ◽  
Luis Rodríguez-Piazza
Keyword(s):  
Analytic Functions ◽  
Spaces Of Analytic Functions

scholarly journals QKtype spaces of analytic functions

2006 ◽  
Vol 4 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Hasi Wulan ◽  
Jizhen Zhou
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Nondecreasing Function ◽  
Necessary And Sufficient Conditions ◽  
Type Space ◽  
Necessary And Sufficient ◽  
Spaces Of Analytic Functions

For a nondecreasing functionK:[0,8)?[0,8)and0<p<8,-2<q<8, we introduceQK(p,q), aQKtype space of functions analytic in the unit disk and study the characterizations ofQK(p,q). Necessary and sufficient conditions onKsuch thatQK(p,q)become some known spaces are given.

Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions

1999 ◽  
Vol 42 (2) ◽  
pp. 139-148 ◽  
Author(s):  
José Bonet ◽  
Paweł Dománski ◽  
Mikael Lindström
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Essential Norm ◽  
Weak Compactness ◽  
Weakly Compact ◽  
Point Evaluation ◽  
Weighted Banach Spaces ◽  
Spaces Of Analytic Functions

AbstractEvery weakly compact composition operator between weighted Banach spaces of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

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