Approximations of holomorphic functions in certain banach spaces
2004 (English)In: International Journal of Mathematics, ISSN 0129-167X, Vol. 15, no 5, 467-471 p.Article in journal (Refereed) Published
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.
Banach spaces, Holomorphic functions
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-45695DOI: 10.1142/S0129167X04002387OAI: oai:DiVA.org:liu-45695DiVA: diva2:266591