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dc.contributor.authorFridman, Buma L.
dc.contributor.authorMa, Daowei
dc.contributor.authorNeelon, Tejinder S.
dc.identifier.citationFridman, Buma L.; Ma, Daowei; Neelon, Tejinder S. 2012. On convergence sets of divergent power series. Annales Polonici Mathematici, v.106 pp.193-198en_US
dc.descriptionClick on the DOI link to access the article (may not be free.)en_US
dc.description.abstractA nonlinear generalization of convergence sets of formal power series, in the sense of Abhyankar-Moh [J. Reine Angew. Math. 241 (1970)], is introduced. Given a family y = phi(s)(t, x) = sb(1)(x)t + b(2)(x)t(2) + ... of analytic curves in C x C-n passing through the origin, Conv(phi)(f) of a formal power series f (y, t, x) is an element of C[[y, t, x]] is defined to be the set of all s is an element of C for which the power series f(phi(s)(t, x), t, x) converges as a series in (t, x). We prove that for a subset E subset of C there exists a divergent formal power series f(y, t, x) is an element of C[[y, t, x]] such that E = Conv(phi)(f) if and only if E is an F-sigma set of zero capacity. This generalizes the results of P. Lelong and A. Sathaye for the linear case phi(s)(t, x) = st.en_US
dc.publisherPolish Academy of Sciences Institute of Mathematicsen_US
dc.relation.ispartofseriesAnnales Polonici Mathematici;v.106
dc.titleOn convergence sets of divergent power seriesen_US
dc.description.versionPeer reviewed

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