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Field name	Details
Dewey Class	515.73
Title	A Primer of Real Analytic Functions ([EBook]) / by Steven G. Krantz, Harold R. Parks.
Author	Krantz, Steven George , 1951-
Added Personal Name	Parks, Harold R.
Other name(s)	SpringerLink (Online service)
Edition statement	Second Edition.
Publication	Boston, MA : Birkhäuser , 2002.
Physical Details	XIII, 209 pages : online resource.
Series	Birkhäuser Advanced Texts / Basler Lehrbücher
ISBN	9780817681340
Summary Note	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.:
Contents note	1 Elementary Properties -- 1.1 Basic Properties of Power Series -- 1.2 Analytic Continuation -- 1.3 The Formula of Faà 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 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 -- 6.5.1 Basic Definitions.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-8176-8134-0
Links to Related Works	Subject References: Algebraic Geometry . Analysis (Mathematics) . Functions of a Complex Variable . Functions of complex variables . Mathematical analysis . Partial differential equations . Authors: author . Krantz, Steven George 1951- . Parks, Harold R. . Corporate Authors: SpringerLink (Online service) . Series: Birkhäuser Advanced Texts / Basler Lehrbücher . Classification: 515.73 . 515.73 (DDC 22) .

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A Primer of Real Analytic Functions

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