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U-Operators

Part of: Special classes of linear operators General theory of linear operators Miscellaneous topics of analysis in the complex domain Integral, integro-differential, and pseudodifferential operators Operator theory: Ordinary differential operators

Published online by Cambridge University Press:  09 April 2009

L. Bernal-González  and
J. A. Prado-Tendero
L. Bernal-González
Affiliation:
Departmento de Análisis Matemático, Facultad de Mathemáticas, Apdo. 1160, Avenida Reina Mercedes, 41080 Sevilla, Spain e-mail: lbernal@us.es, tendero@us.es
J. A. Prado-Tendero
Affiliation:
Departmento de Análisis Matemático, Facultad de Mathemáticas, Apdo. 1160, Avenida Reina Mercedes, 41080 Sevilla, Spain e-mail: lbernal@us.es, tendero@us.es
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Abstract

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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.

Keywords

universal functiongap seriescomposition operatordifferential operatorintegral operatorTaylor shiftU-operator

MSC classification

Secondary: 30E10: Approximation in the complex domain 47A16: Cyclic vectors, hypercyclic and chaotic operators 47B33: Composition operators 47B38: Operators on function spaces (general) 47E05: Ordinary differential operators (should also be assigned at least one other classification number in section 47) 47G10: Integral operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 78 , Issue 1 , February 2005 , pp. 59 - 90
Copyright
Copyright © Australian Mathematical Society 2005

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