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A primer of real analytic functions /

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Bibliographic Details
Main Author:	Krantz, Steven G. (Steven George), 1951- (Author)
Other Authors:	Parks, Harold R., 1949-
Format:	Book
Language:	English
Published:	Boston : Birkhäuser, [2002]
Edition:	2nd ed.
Series:	Birkhäuser advanced texts.
Subjects:	Functions of real variables. Mathematical analysis. Fonctions de variables réelles. Analyse mathématique. Analytische Funktion Reelle Funktion Fonctions analytiques. Reelle Funktion > Analytische Funktion. Analytische Funktion > Reelle Funktion.
Online Access:	Table of contents Table of contents Table of contents Table of contents Publisher description Cover http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=1479038&custom_att_2=simple_viewer

Table of Contents:

1. Elementary Properties
1.1. Basic Properties of Power Series
1.2. Analytic Continuation
1.3. The Formula of Faa di Bruno
1.4. Composition of Real Analytic Functions
1.5. Inverse Functions
2. Multivariable Calculus of Real Analytic Functions
2.1. Power Series in Several Variables
2.2. Real Analytic Functions of Several Variables
2.3. The Implicit Function Theorem
2.4. A Special Case of the Cauchy-Kowalewsky Theorem
2.5. The Inverse Function Theorem
2.6. Topologies on the Space of Real Analytic Functions
2.7. Real Analytic Submanifolds
2.8. The General Cauchy-Kowalewsky Theorem
3. Classical Topics
3.0. Introductory Remarks
3.1. The Theorem of Pringsheim and Boas
3.2. Besicovitch's Theorem
3.3. Whitney's Extension and Approximation Theorems
3.4. The Theorem of S. Bernstein
4. Some Questions of Hard Analysis
4.1. Quasi-analytic and Gevrey Classes
4.2. Puiseux Series
4.3. Separate Real Analyticity
5. Results Motivated by Partial Differential Equations
5.1. Division of Distributions I
5.2. Division of Distributions II
5.3. The FBI Transform
5.4. The Paley-Wiener Theorem
6. Topics in Geometry
6.1. The Weierstrass Preparation Theorem
6.2. Resolution of Singularities
6.3. Lojasiewicz's Structure Theorem for Real Analytic Varieties
6.4. The Embedding of Real Analytic Manifolds
6.5. Semianalytic and Subanalytic Sets.