J. Aust. Math. Soc.  78 (2005), 59-89
U-operators

L. Bernal-González
  Departamento de Análisis Matemático
  Facultad de Matemáticas, Apdo. 1160
  Avenida Reina Mercedes
  41080 Sevilla
  Spain
  lbernal@us.es
and
J. A. Prado-Tendero
  Departamento de Análisis Matemático
  Facultad de Matemáticas, Apdo. 1160
  Avenida Reina Mercedes
  41080 Sevilla
  Spain
  tendero@us.es


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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