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Approximations of holomorphic functions in certain banach spaces
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
2004 (English)In: International Journal of Mathematics, ISSN 0129-167X, Vol. 15, no 5, 467-471 p.Article in journal (Refereed) Published
Abstract [en]

Let E be a Banach space and let B(R) ? E denote the open ball with centre at 0 and radius R. The following problem is studied: given 0 < r < R, ? > 0 and a function f holomorphic on B(R), does there always exist an entire function g on E such that abs(f - g) < ? on B (r)? L. Lempert has proved that the answer is positive for Banach spaces having an unconditional basis with unconditional constant 1. In this paper a somewhat shorter proof of Lemperts result is given. In general it is not possible to approximate f by polynomials since f does not need to be bounded on B(r).

Place, publisher, year, edition, pages
2004. Vol. 15, no 5, 467-471 p.
Keyword [en]
Banach spaces, Holomorphic functions
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-45695DOI: 10.1142/S0129167X04002387OAI: diva2:266591
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-12

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Josefson, Bengt
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