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A primer of real analytic functions. 2nd ed. (English) Zbl 1015.26030
Birkhäuser Advanced Texts. Basler Lehrbücher. Boston, MA: Birkhäuser. xiv, 205 p. (2002).
From the preface to the second edition: “The theory of real analytic functions is the wellspring of mathematical analysis. It is remarkable that this is the first book on the subject, and we want to keep it up to date and as correct as possible.
With these thoughts in mind, we have utilized helpful remarks and criticisms from many readers and have thereby made numerous emendations. We have also added material. There is a now a treatment of the Weierstrass preparation theorem, a new argument to establish Hensel’s lemma and Puiseux’s theorem, a new treatment of Faà di Bruno’s formula, a thorough discussion of topologies on spaces of real analytic functions, and a second independent argument for the implicit function theorem. We trust that these new topics will make the book more complete, and hence a more useful reference.”
See the review of the first edition (1992) in Zbl 0767.26001, too.

26E05 Real-analytic functions
26-02 Research exposition (monographs, survey articles) pertaining to real functions
26E10 \(C^\infty\)-functions, quasi-analytic functions
32C05 Real-analytic manifolds, real-analytic spaces
14P15 Real-analytic and semi-analytic sets