Abstract
In this short paper, we study the existence of common universal series for uncountable families of specific linear operators. In particular we deal with some derived forms of Seleznev’s theorem and we obtain common universal elements in the space of formal power series in several complex variables.
Similar content being viewed by others
References
Abakumov E., Gordon J.: Common hypercyclic vectors for multiples of backward shift. J. Funct. Anal. 200, 494–504 (2003)
Aron R. et al.: Operators with common hypercyclic subspaces. J. Operator Theory 54, 251–260 (2005)
Bayart F.: Topological and algebraic genericity of divergence and universality. Studia Math. 167, 161–181 (2005)
Bayart F. et al.: Abstract theory of universal series and applications. Proc. London Math. Soc. 96, 417–463 (2008)
F. Bayart and E. Matheron, Dynamics of linear operators, Cambridge tracts in Mathematics 179, Cambridge University Press, Cambridge, 2009.
R. Clouâtre, Universal power series in \({{\mathbb{C}}^N}\), preprint (2010).
Conejero J.A., Müller V., Peris A.: Hypercyclic behaviour of operators in a hypercyclic C 0-semigroup. J. Funct. Anal. 244, 342–348 (2007)
Costakis G., Sambarino M.: Genericity of wild holomorphic functions and common hypercyclic vectors. Adv. Math. 182, 278–306 (2004)
Demanze O., Mouze A.: On universal formal power series. J. Math. Anal. Appl. 338, 662–674 (2008)
Grosse-Erdmann K.-G.: Universal families and hypercyclic operators. Bull. Amer. Math. Soc. 36, 345–381 (1999)
León-Saavedra F., Müller V.: Rotations of hypercyclic and supercyclic operators. Integral Equations Operator Theory 50, 385–391 (2004)
Luh W.: Approximation analytischer Funktionen durch überkonvergente Potenzreihen und deren Matrix-Transformierten. Mitt. Math. Sem. Giessen 88, 1–56 (1970)
MouzeA. Nestoridis V.: Universality and ultradifferentiable functions: Fekete’s Theorem. Proc. Amer. Math. Soc. 138, 3945–3955 (2010)
G. Pál, Zwei kleine Bemerkungen, Tohoku Math. J. 6 (1914/15), 42–43.
Papadimitropoulos C.: Common dense hypercyclic manifolds for translation and dilatation operators. Complex Var. Elliptic Equ. 53, 383–390 (2008)
Seleznev A.I.: On universal power series. Math. Sbornik N.S. 28, 453–460 (1951)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mouze, A. Common universal restrictions of power series. Arch. Math. 96, 161–168 (2011). https://doi.org/10.1007/s00013-010-0210-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-010-0210-5