科研之友
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摘要
We show how to solve explicitly an equation satisfied by a real function belonging to certain general quasianalytic classes. More precisely, we show that if f (x(1),..,xm, y) belongs to such a class, then the solutions y = phi (x(1),...x(m)) of the equation f = 0 in a neighbourhood of the origin can be expressed, piecewise, as finite compositions of functions in the class, taking nth roots and quotients. Examples of the classes under consideration are the collection of convergent generalised power series, a class of functions which contains some Dulac Transition Maps of real analytic planar vector fields, quasianalytic Denjoy-Carleman classes and the collection of multisummable series.
- 出版日期2015
