A Primer of Real Analytic Functions

Steven G. Krantz

ISBN 10: 0817642641 / ISBN 13: 9780817642648

Editore: Birkhäuser, Birkhäuser, 2002

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Druck auf Anfrage Neuware - Printed after ordering - 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 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.

Codice articolo 9780817642648

Dati bibliografici

• Titolo: A Primer of Real Analytic Functions
• Editore: Birkhäuser, Birkhäuser
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 0817642641
• ISBN 13: 9780817642648
• Rilegatura: Buch
• Edizione: seconda edizione
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 17 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 17 millimetri di profondità
• Peso: 512 grammi

Descrizione articolo

Riassunto

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, Faa de 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 Faa de Bruno formula; Topologies on the space of real analytic functions; Alternative characterizations of real analytic functions; Surjectivity of partial differential operators; The Weierstrass Preparation Theorem

Recensione

"This is the second, improved edition of the only existing monograph devoted to real-analytic functions, whose theory is rightly considered in the preface 'the wellspring of mathematical analysis.' Organized in six parts, [with] a very rich bibliography and an index, this book is both a map of the subject and its history. Proceeding from the most elementary to the most advanced aspects, it is useful for both beginners and advanced researchers. Names such as Cauchy-Kowalewsky (Kovalevskaya), Weierstrass, Borel, Hadamard, Puiseux, Pringsheim, Besicovitch, Bernstein, Denjoy-Carleman, Paley-Wiener, Whitney, Gevrey, Lojasiewicz, Grauert and many others are involved either by their results or by their concepts."

―MATHEMATICAL REVIEWS

"Bringing together results scattered in various journals or books and presenting them in a clear and systematic manner, the book is of interest first of all for analysts, but also for applied mathematicians and researchers in real algebraic geometry."

―ACTA APPLICANDAE MATHEMATICAE