Spaces of holomorphic functions in regular domains |
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Authors: | M Valdivia |
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Institution: | aDepartamento de Análisis Matemático, Universidad de Valencia, Dr. Moliner 50, 46100 Burjasot, Valencia, Spain |
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Abstract: | Let Ω be a regular domain in the complex plane , . Let be the linear space over of the holomorphic functions f in Ω such that f(n) is bounded in Ω and is continuously extendible to the closure of Ω, n=0,1,2,… . We endow , in a natural manner, with a structure of Fréchet space and we obtain dense subspaces F of , with good topological linear properties, also satisfying that each function f of F, distinct from zero, does not extend holomorphically outside Ω. |
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Keywords: | Extensions of holomorphic functions Regular complex domains Dense-lineability |
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