Analytic completion of an open set



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Ansemil, José María M. and López-Salazar Codes, Jerónimo and Ponte, Socorro (2012) Analytic completion of an open set. In Contribuciones matemáticas en honor a Juan Tarrés. UCM, Madrid, pp. 27-38. ISBN 978-84-695-4421-1

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Let f be a holomorphic function on a complex normed space E. The possibility of extending f to the completion of E has been studied by Hirschowitz, Noverraz, Dineen, and Dineen-Noverraz. Here, following the ideas in [4, section 6.1], we study the extension problem for functions defined on open subsets of E. Moreover, through a complexification process, we use these results to obtain the analogous ones for analytic functions on real normed spaces. We note that in the real case we do not have, among other things, Cauchy inequalities and they are essential in the complex case.

Item Type:Book Section
Uncontrolled Keywords:Normed space; Holomorphic function; Bounding set
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:17342
Deposited On:05 Dec 2012 12:51
Last Modified:01 Jan 2021 00:01

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