A Primer of Real Analytic Functions / Edition 2

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Overview

Key topics in the theory of real analytic functions are covered in this text,and are rather difficult to pry out of the mathematics literature.; This expanded and updated 2nd ed. will be published out of Boston in Birkhäuser Adavaned Texts series.; Many historical remarks, examples, references and an excellent index should encourage the reader study this valuable and exciting theory.; Superior advanced textbook or monograph for a graduate course or seminars on real analytic functions.; New to the second edition a revised and comprehensive treatment of the Faá de Bruno formula, topologies on the space of real analytic functions,; alternative characterizations of real analytic functions, surjectivity of partial differential operators, And the Weierstrass preparation theorem.

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Editorial Reviews

From the Publisher
"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

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Product Details

  • ISBN-13: 9780817642648
  • Publisher: Birkhauser Verlag
  • Publication date: 6/27/2002
  • Series: Birkhauser Advanced Texts Basler Lehrbucher Series
  • Edition description: 2nd ed. 2002
  • Edition number: 2
  • Pages: 209
  • Sales rank: 1,136,512
  • Product dimensions: 0.56 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Preface to the Second Edition
• Preface to the First Edition
• Elementary Properties
• Multivariable Calculus of Real Analytic Functions
• Classical Topics
• Some Questions of Hard Analysis
• Results Motivated by Partial Differential Equations
• Topics in Geometry
• Bibliography
• Index

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