We give a survey about the Runge approximation problem for a holomorphic function defined on the unit ball of a complex Banach space. More precisely, we ask whether such a holomorphic function can be uniformly approximated on smaller balls by functions that are holomorphic on the entire space. This turns out to be a subtle (open) question, whose (partial) resolution in the past 15 years played a central role in deeper investigations in complex analysis in Banach spaces.
CITATION STYLE
Meylan, F. (2015). Holomorphic approximation in banach spaces: A survey. In Springer Proceedings in Mathematics and Statistics (Vol. 127, pp. 231–240). Springer New York LLC. https://doi.org/10.1007/978-3-319-17443-3_13
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