## A Primer of Real Analytic FunctionsIt is a pleasure and a privilege to write this new edition of A Primer 0/ Real Ana lytic Functions. The theory of real analytic functions is the wellspring of mathe matical 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 treat ment of Faa di Bruno's forrnula, a thorough discussion of topologies on spaces of real analytic functions, and a second independent argument for the implicit func tion theorem. We trust that these new topics will make the book more complete, and hence a more useful reference. It is a pleasure to thank our editor, Ann Kostant of Birkhäuser Boston, for mak ing the publishing process as smooth and trouble-free as possible. We are grateful for useful communications from the readers of our first edition, and we look for ward to further constructive feedback. |

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algebraic analysis analytic variety apply assume common factor complement complex analytic connected component consider coordinate Corollary deﬁned Deﬁnition degree denote dimension domain embedding estimate Euclidean exist f is real fact ﬁeld ﬁmction ﬁnd ﬁnite ﬁrst ﬁxed follows formula Fourier transform func function deﬁned function f Gevrey class Hardcover holds holomorphic functions hypothesis implicit function theorem induction inequality inﬁnitely differentiable interval of convergence inverse function theorem ISBN Lemma Let f linear multiindex multiindices neighborhood nonnegative integers notation obtain open interval open set open subset origin positive constants positive integer Proposition prove Puiseux’s theorem quasi-analytic radius of convergence real analytic functions real analytic manifold real analytic submanifold real numbers real roots real variables result sequence of real series converges singularities smooth space speciﬁc strictly less subanalytic sufﬁce sufﬁciently Suppose symmetric tempered distribution theory tion vanish identically vector Weierstrass preparation theorem Whitney zero set