A Primer of Real Analytic Functions - Krantz, Steven G. 1951- (Birkhäuser Boston, 2002)
It is a pleasure and a privilege to write this new edition of A Primer of Real Analytic Functions. 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 Faa 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. It is a pleasure to thank our editor, Ann Kostant of Birkhäuser Boston, for making 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 forward to further constructive feedback