Author | Krantz, Steven G. author |
---|---|
Title | A Primer of Real Analytic Functions [electronic resource] / by Steven G. Krantz, Harold R. Parks |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2002 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-0-8176-8134-0 |
Descript | XIII, 209 p. online resource |
1 Elementary Properties -- 1.1 Basic Properties of Power Series -- 1.2 Analytic Continuation -- 1.3 The Formula of Faร 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 ofPringsheim and Boas -- 3.2 Besicovitchโs Theorem -- 3.3 Whitneyโs 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 Lojasiewiczโs Structure Theorem for Real Analytic Varieties -- 6.4 The Embedding of Real Analytic Manifolds -- 6.5 Semianalytic and Subanalytic Sets -- 6.5.1 Basic Definitions