dc.contributor.author Fridman, Buma L. dc.contributor.author Ma, Daowei dc.contributor.author Neelon, Tejinder S. dc.date.accessioned 2013-07-08T15:10:01Z dc.date.available 2013-07-08T15:10:01Z dc.date.issued 2012 dc.identifier.citation Fridman, Buma L.; Ma, Daowei; Neelon, Tejinder S. 2012. On convergence sets of divergent power series. Annales Polonici Mathematici, v.106 pp.193-198 en_US dc.identifier.issn 0066-2216 dc.identifier.other WOS:000311525700014 dc.identifier.uri http://dx.doi.org/10.4064/ap106-0-14 dc.identifier.uri http://hdl.handle.net/10057/5872 dc.description Click on the DOI link to access the article (may not be free.) en_US dc.description.abstract A 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.language.iso en_US en_US dc.publisher Polish Academy of Sciences Institute of Mathematics en_US dc.relation.ispartofseries Annales Polonici Mathematici;v.106 dc.title On convergence sets of divergent power series en_US dc.type Article en_US dc.description.version Peer reviewed
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