A Primer of Real Analytic Functions

Harold R. Parks

ISBN 10: 0817642641 / ISBN 13: 9780817642648

Editore: Birkhäuser Boston Jun 2002, 2002

Riguardo questo articolo

This item is printed on demand - it takes 3-4 days longer - Neuware -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, Faà 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 Faà 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. 228 pp. Englisch.

Codice articolo 9780817642648

Dati bibliografici

• Titolo: A Primer of Real Analytic Functions
• Editore: Birkhäuser Boston Jun 2002
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 0817642641
• ISBN 13: 9780817642648
• Rilegatura: Buch
• Edizione: seconda edizione
• Condizione: Neu

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