Article
Holomorphic T-monsters and strongly omnipresent operators
Author/s | Bernal González, Luis
Calderón Moreno, María del Carmen |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2000-06 |
Deposit Date | 2019-06-18 |
Published in |
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Abstract | Assume that G is a nonempty open subset of the complex plane and that T is an operator on the linear space of holomorphic functions in G,
endowed with the compact-open topology. In this paper we introduce the notions of ... Assume that G is a nonempty open subset of the complex plane and that T is an operator on the linear space of holomorphic functions in G, endowed with the compact-open topology. In this paper we introduce the notions of strongly omnipresent operator and of T-monster, which are related to the wild behaviour of certain holomorphic functions near the boundary of G. T-monsters extend a concept introduced by W. Luh and K.-G. Grosse-Erdmann. After showing that T is strongly omnipresent if and only if the set of T-monsters is residual, it is proved in this paper that certain kinds of infinite order differential and antidifferential operators are strongly omnipresent, which improves some earlier nice results due to the mentioned authors. |
Project ID. | PB96-1348 |
Citation | Bernal González, L. y Calderón Moreno, M.d.C. (2000). Holomorphic T-monsters and strongly omnipresent operators. Journal of Approximation Theory, 104 (2), 204-219. |
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