Holomorphic Operators Generating Dense Images |
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Authors: | L Bernal-González M C Calderón-Moreno J A Prado-Bassas |
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Institution: | (1) Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Avda. Reina Mercedes, 41080 Sevilla, Spain |
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Abstract: | The existence of infinite dimensional closed linear spaces of holomorphic functions f on a domain G in the complex plane such that Tf has dense images on certain subsets of G, where T is a continuous linear operator, is analyzed. Necessary and sufficient conditions for T to have the latter property are provided and applied to obtain a number of concrete examples: infinite order differential
operators, composition operators and multiplication operators, among others.
This work was supported in part by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127 and by MEC DGES Grants
MTM2006-13997-C02-01 and MTM2004-21420-E. |
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Keywords: | Primary 47B38 Secondary 30D40 47B33 47E05 |
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