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A primer of real analytic functions

Author: Steven G Krantz; Harold R Parks
Publisher: Basel ; Boston : Birkhäuser Verlag, 1992.
Series: Basler Lehrbücher, vol. 4.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
The subject of real analytic functions is one of the oldest in mathe℗Ư matical analysis. Today it is encountered early in ones mathematical training: the first taste usually comes in calculus. While most work℗Ư ing mathematicians use real analytic functions from time to time in their work, the vast lore of real analytic functions remains obscure and buried in the literature. It is remarkable that the most accessible  Read more...
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Genre/Form: Electronic books
Reell-analytische Funktion
Additional Physical Format: Print version:
Krantz, Steven G. (Steven George), 1951-
Primer of real analytic functions.
Basel ; Boston : Birkhäuser Verlag, 1992
(DLC) 92019718
(OCoLC)26014558
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Steven G Krantz; Harold R Parks
ISBN: 9783034876445 3034876440
OCLC Number: 681846186
Reproduction Notes: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010. MiAaHDL
Description: 1 online resource (x, 184 pages) : illustrations.
Details: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Contents: 1. Elementary Properties --
2. Classical Topics --
3. Some Questions of Hard Analysis --
4. Results Motivated by Partial Differential Equations --
5. Topics in Geometry.
Series Title: Basler Lehrbücher, vol. 4.
Responsibility: Steven G. Krantz, Harold R. Parks.

Abstract:

The subject of real analytic functions is one of the oldest in mathe℗Ư matical analysis. Today it is encountered early in ones mathematical training: the first taste usually comes in calculus. While most work℗Ư ing mathematicians use real analytic functions from time to time in their work, the vast lore of real analytic functions remains obscure and buried in the literature. It is remarkable that the most accessible treatment of Puiseux's theorem is in Lefschetz's quite old Algebraic Geometry, that the clearest discussion of resolution of singularities for real analytic manifolds is in a book review by Michael Atiyah, that there is no comprehensive discussion in print of the embedding prob℗Ư lem for real analytic manifolds. We have had occasion in our collaborative research to become ac℗Ư quainted with both the history and the scope of the theory of real analytic functions. It seems both appropriate and timely for us to gather together this information in a single volume. The material presented here is of three kinds. The elementary topics, covered in Chapter 1, are presented in great detail. Even results like a real ana℗Ư lytic inverse function theorem are difficult to find in the literature, and we take pains here to present such topics carefully. Topics of middling difficulty, such as separate real analyticity, Puiseux series, the FBI transform, and related ideas (Chapters 2-4), are covered thoroughly but rather more briskly.

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