| A Primer of Real Analytic Functions Contributor(s): Krantz, Steven G. (Author), Parks, Harold R. (Author) |
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ISBN: 0817642641 ISBN-13: 9780817642648 Publisher: Birkhauser OUR PRICE: $94.99 Product Type: Hardcover - Other Formats Published: June 2002 Annotation: The subject of real analytic functions is one of the oldest in modern mathematics and is the wellspring of the theory of analysis, both real and complex. To date, there is no comprehensive book on the subject, yet the tools of the theory are widely used by mathematicians today. Key topics in the theory of real analytic functions that are covered in this text and are rather difficult to pry out of the literature include: the real analytic implicit function theorem, resolution of singularities, the FBI transform, semi-analytic sets, Fa? di Bruno's formula and its applications, zero sets of real analytic functions, Lojaciewicz's theorem, Puiseaux's theorem. New to this second edition are such topics as: * A more revised and comprehensive treatment of the Fa? di Bruno formula * An alternative treatment of the implicit function theorem * Topologies on the space of real analytic functions * The Weierstrass Preparation Theorem This well organized and clearly written advanced textbook introduces students to real analytic functions of one or more real variables in a systematic fashion. The first part focuses on elementary properties and classical topics and the second part is devoted to more difficult topics. Many historical remarks, examples, references and an excellent index should encourage student and researcher alike to further study this valuable and exciting theory. |
| Additional Information |
| BISAC Categories: - Mathematics | Calculus - Mathematics | Mathematical Analysis - Mathematics | Geometry - Algebraic |
| Dewey: 515 |
| LCCN: 2002021565 |
| Series: Birkhäuser Advanced Texts Basler Lehrbücher |
| Physical Information: 0.69" H x 6.84" W x 9.02" (1.18 lbs) 209 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: It 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 Birkh user 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. |