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Search: MSC category 47A16 ( Cyclic vectors, hypercyclic and chaotic operators )

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1. CMB 2012 (vol 56 pp. 477)

Ayadi, Adlene
Hypercyclic Abelian Groups of Affine Maps on $\mathbb{C}^{n}$
We give a characterization of hypercyclic abelian group $\mathcal{G}$ of affine maps on $\mathbb{C}^{n}$. If $\mathcal{G}$ is finitely generated, this characterization is explicit. We prove in particular that no abelian group generated by $n$ affine maps on $\mathbb{C}^{n}$ has a dense orbit.

Keywords:affine, hypercyclic, dense, orbit, affine group, abelian
Categories:37C85, 47A16

2. CMB 2008 (vol 51 pp. 378)

Izuchi, Kou Hei
Cyclic Vectors in Some Weighted $L^p$ Spaces of Entire Functions
In this paper, we generalize a result recently obtained by the author. We characterize the cyclic vectors in $\Lp$. Let $f\in\Lp$ and $f\poly$ be contained in the space. We show that $f$ is non-vanishing if and only if $f$ is cyclic.

Keywords:weighted $L^p$ spaces of entire functions, cyclic vectors
Categories:47A16, 46J15, 46H25

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