http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
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.
Includes bibliographical references (pages 187-201) and index.
Boston, MA : Birkhäuser Boston : Imprint : Birkhäuser, 2002