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HYPERCYCLICITY FOR TRANSLATIONS THROUGH RUNGE`S THEOREM
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 Title & Authors
HYPERCYCLICITY FOR TRANSLATIONS THROUGH RUNGE`S THEOREM
Hallack Andre Arbex;
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 Abstract
In this paper, we first adapt Runge`s Theorem to work on certain domains in any complex Banach space. Then, using this result, we extend Birkhoff`s Theorem on the hypercyclicity of translations on and Costakis` and Sambarino`s result on the existence of common hypercyclic functions for uncountable families of translations on to subs paces of (in some cases all of (E)), E being in a large class of Banach spaces.
 Keywords
hypercyclic operators;hypercyclicity;
 Language
English
 Cited by
 References
1.
R. Aron, Weakly uniformly continuous and weakly sequentially continuous entire func-tions, Advances in holomorphy (Proc. Sem. Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1977), North-Holland Math. Studies, 34. North-Holland, Amsterdam (1979), 47-66

2.
R. Aron and D. Markose, On universal functions, J. Korean Math. Soc. 41 (2004), no. 1, 65-76 crossref(new window)

3.
G. Birkhoff, Demonstration d'un theoreme elementaire sur les fonctions entieres, Cr. R. Acad. Sci. Paris 189 (1929), 473-475

4.
J. Conway, A course in functional analysis, Graduate Texts in Mathematics, 96. Springer-Verlag, New York, 1990

5.
G. Costakis and M. Sambarino, Genericity of wild holomorphic functions and common hypercyclic vectors, Adv. Math. 182 (2004), no. 2, 278-306 crossref(new window)

6.
K.-G. Grosse-Erdmann, Universal families and hypercyclic operators, Bull. Amer. Math. Soc. (N. S.) 36 (1999), no. 3, 345-381 crossref(new window)

7.
J. Mujica, Complex Analysis in Banach Spaces, North-Holland Mathematics Studies 120, North-Holland Publishing Co., 1986