JOURNAL BROWSE
Search
Advanced SearchSearch Tips
HYPERCYCLICITY FOR TRANSLATIONS THROUGH RUNGE'S THEOREM
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
HYPERCYCLICITY FOR TRANSLATIONS THROUGH RUNGE'S THEOREM
Hallack Andre Arbex;
  PDF(new window)
 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