Analytical Properties of Power Series on Levi-Civita Fields
AbstractA detailed study of power series on the Levi-Civita fields is presented. After
reviewing two types of convergence on those fields, including convergence
criteria for power series, we study some analytical properties of power
series. We show that within their domain of convergence, power series are
infinitely often differentiable and re-expandable around any point within the
radius of convergence from the origin. Then we study a large class of
functions that are given
locally by power series and contain all the continuations of real power
series. We show that these functions have similar properties as real analytic
functions. In particular, they are closed under arithmetic operations and
composition and they are infinitely often differentiable.
K. Shamseddine, M. Berz,
Annales Mathematiques Blaise Pascal 12 (2005) 309-329
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