# EXISTENCE OF COMMON HYPERCYCLIC VECTORS FOR TRANSLATION OPERATORS

@article{Tsirivas2014EXISTENCEOC, title={EXISTENCE OF COMMON HYPERCYCLIC VECTORS FOR TRANSLATION OPERATORS}, author={N. Tsirivas}, journal={arXiv: Complex Variables}, year={2014} }

Let H(C) be the set of entire functions endowed with the topology Tu of local uniform convergence. Fix a sequence of non-zero complex numbers (�n) with |�n| → +∞ and |�n+1|/|�n| → 1. We prove that there exists a residual set G ⊂ H(C) such that for every f ∈ G and every non-zero complex number a the set {f(z + �na) : n = 1,2,...} is dense in (H(C),Tu). This provides a very strong extension of a theorem due to Costakis and Sambarino in (23). Actually, in (23) the above result is proved only for…

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