Submission date: 30 March 2013.

Abstract:

A generalised power series (in several variables) is a series with real nonnegative exponents whose support is contained in a cartesian product of well-ordered subsets of the positive real half-line. We show that, if f is a convergent generalised power series in n+1 variables, then the solutions of the equation f=0 with respect to the last variable can be obtained as finite compositions of convergent generalised power series and quotients. We prove a similar result for functions belonging to quasianalytic Denjoy-Carleman classes and for certain Gevrey functions in several variables.

Mathematics Subject Classification: 30D60, 14P15, 32S45

Keywords and phrases:

Full text arXiv 1304.0108: pdf, ps.