Domains of analyticity in real normed spaces (Q1260876)

Let \(E\) be a separable real normed space and \(M\) a subset. The authors construct a \({\mathcal C}^ \infty\)-function on \(E\) which is analytic on \(E\setminus M\) and analytic at no point of \(M\) and such that its restriction to \(E\setminus M\) has no analytic extension at any boundary point of \(M\) under either of the following conditions: 1) \(E\) satisfies the Kurzweil condition i.e. there is a polynomial \(P\) on \(E\) with \(P(0)=0\) and which is bounded away from 0 on the unit sphere of \(E\), 2) \(M\) is a weakly closed subset of \(E\). Meanwhile the authors have obtained some stronger results in Bull. Pol. Acad. Sci., Math. 41, No. 2, 131-137 (1993; Zbl 0799.46048).