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    2015. Lineability.


    Bernal-González, Luis 2013. Compositionally Universal Entire Functions on the Plane and the Punctured Plane. Complex Analysis and Operator Theory, Vol. 7, Issue. 3, p. 577.


    Vogt, Andreas 2012. On Bounded Universal Functions. Computational Methods and Function Theory, Vol. 12, Issue. 1, p. 213.


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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society, Volume 78, Issue 1
  • February 2005, pp. 59-90

U-Operators

  • L. Bernal-González (a1) and J. A. Prado-Tendero (a1)
  • DOI: http://dx.doi.org/10.1017/S1446788700015561
  • Published online: 01 April 2009
Abstract
Abstract

Inspired by a statement of W. Luh asserting the existence of entire functions having together with all their derivatives and antiderivatives some kind of additive universality or multiplicative universality on certain compact subsets of the complex plane or of, respectively, the punctured complex plane, we introduce in this paper the new concept of U-operators, which are defined on the space of entire functions. Concrete examples, including differential and antidifferential operators, composition, multiplication and shift operators, are studied. A result due to Luh, Martirosian and Müller about the existence of universal entire functions with gap power series is also strengthened.

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[3]L. Bernal-González , ‘Universal functions for Taylor shifts’, Complex Variables 31 (1996), 121129.

[4]L. Bernal-González , ‘Hypercyclic sequences of differential and antidifferential operators’, J. Approx. Theory 96 (1999), 323337.

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[14]M. C. Calderón-Moreno , ‘Holomorphic differential operators and plane sets with dense images’, Complex Variables 47 (2002), 167176.

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  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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