Universality of holomorphic functions bounded on closed sets |
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Authors: | L Bernal-González A Bonilla |
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Institution: | a Departamento de Análisis Matemático, Avda. Reina Mercedes, Apdo. 1160, 41080-Sevilla, Spain b Departamento de Análisis Matemático, Facultad de Matemáticas, C/Astrofísico Fco. Sánchez, s/n, 38271-La Laguna, Tenerife, Canary Islands, Spain |
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Abstract: | In this note, the existence of translation-universal entire functions which are bounded on certain closed subsets is characterized in terms of topological and geometrical properties of such subsets. Corresponding results are also stated in the space of holomorphic functions on the unit disk and in the space of harmonic functions on the plane. Moreover, it is shown the existence of entire functions which are bounded on many rays and, simultaneously, are universal with respect to a prescribed infinite-order differential operator. |
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Keywords: | Universal function Arakelian set Bounded holomorphic function Inscribed radius Infinite-order differential operator |
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