Birkhäuser Advanced Texts Basler Lehrbücher

A Primer of Real Analytic Functions

Authors: Krantz, Steven G, Parks, Harold R.

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About this Textbook

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.

Reviews

"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


Table of contents (6 chapters)

  • Elementary Properties

    Krantz, Steven G. (et al.)

    Pages 1-23

  • Multivariable Calculus of Real Analytic Functions

    Krantz, Steven G. (et al.)

    Pages 25-66

  • Classical Topics

    Krantz, Steven G. (et al.)

    Pages 67-81

  • Some Questions of Hard Analysis

    Krantz, Steven G. (et al.)

    Pages 83-113

  • Results Motivated by Partial Differential Equations

    Krantz, Steven G. (et al.)

    Pages 115-149

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-0-8176-8134-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-0-8176-4264-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA
  • ISBN 978-1-4612-6412-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
A Primer of Real Analytic Functions
Authors
Series Title
Birkhäuser Advanced Texts Basler Lehrbücher
Copyright
2002
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-8176-8134-0
DOI
10.1007/978-0-8176-8134-0
Hardcover ISBN
978-0-8176-4264-8
Softcover ISBN
978-1-4612-6412-5
Series ISSN
1019-6242
Edition Number
2
Number of Pages
XIII, 209
Topics