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On Bounded Universal Functions

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Abstract

We investigate boundedness properties of functions that are universal with respect to translations and “multiplicative translations”. It is well known that there exist entire functions which are universal in the sense of Birkhoff and are bounded on every line. We prove a negative result for multiplicative universal functions.

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References

  1. Y. Abe and P. Zappa, Universal functions on complex general linear groups, J. Approx. Theory 100 (1999), 221–232.

    Article  MathSciNet  MATH  Google Scholar 

  2. F. Bayart and E. Matheron, Dynamics of Linear Operators, Cambridge Tracts in Mathematics, Cambridge University Press, 2009.

  3. L. Bernal-González and A. Bonilla, Universality of entire functions bounded on closed sets, J. Math. Anal. Appl. 315 (2006), 302–316.

    Article  MathSciNet  MATH  Google Scholar 

  4. L. Bernal-González and A. Montes-Rodríguez, Universal functions for composition operators, Complex Variables 27 (1995), 47–56.

    Article  MATH  Google Scholar 

  5. L. Bernal-González and J. A. Prado-Tendero, μ-Operators, J. Austral Math. Soc. (Series A) 78 (2005), 59–89.

    Article  MATH  Google Scholar 

  6. G. D. Birkhoff, Démonstration d’une théorème élémentaire sur les fonctions enti`eres, C. R. Acad. Sci. Paris 189 (1929), 473–475.

    MATH  Google Scholar 

  7. M. C. Calderón-Moreno, Universal functions with small derivatives and extremely fast growth, Analysis 22 (2002), 57–66.

    MATH  Google Scholar 

  8. G. Costakis and M. Sambarino, Genericity of wild holomorphic functions and common hypercyclic vectors, Adv. Math. 182 (2004), 278–306.

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Gaier, Lectures on Complex Approximation, Birkhäuser, Boston, 1985.

    Google Scholar 

  10. T. Gharibyan, W. Luh and M. Nieß, Birkhoff functions that are bounded on prescribed sets, Arch. Math. 86 (2006), 261–267.

    Article  MATH  Google Scholar 

  11. K.-G. Grosse-Erdmann, Universal families and hypercyclic operators, Bull. Amer. Math. Soc. 36 (1999), 345–381.

    Article  MathSciNet  MATH  Google Scholar 

  12. K.-G. Grosse-Erdmann and A. Peris, Linear Chaos, Springer, New York, 2011.

    Book  MATH  Google Scholar 

  13. A. S. B. Holland, Introduction to the Theory of Entire Functions, Academic Press, New York, 1973.

    MATH  Google Scholar 

  14. W. Luh, Entire functions with various universal properties, Complex Variables Theory Appl. 31 (1996), 87–96.

    Article  MathSciNet  MATH  Google Scholar 

  15. M. Nieß, Universelle Funktionen mit zusätzlichen Eigenschaften, PhD-dissertation Universität Trier, 2006.

  16. P. Zappa, On universal holomorphic functions, Bolletino U.M.I. A (7) 2 (1988), 345–352.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Mathematics, University of Trier, 54296, Trier, Germany

    Andreas Vogt

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  1. Andreas Vogt
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Correspondence to Andreas Vogt.

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Vogt, A. On Bounded Universal Functions. Comput. Methods Funct. Theory 12, 213–219 (2012). https://doi.org/10.1007/BF03321823

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  • DOI: https://doi.org/10.1007/BF03321823

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