Steven G. Krantz, Harold R. Parks

A Primer of Real Analytic Functions (eBook, PDF)

• Format: PDF

Produktbeschreibung

Key topics in the theory of real analytic functions are covered in this text,and are rather difficult to pry out of the mathematics literature.; This expanded and updated 2nd ed. will be published out of Boston in Birkhäuser Adavaned Texts series.; Many historical remarks, examples, references and an excellent index should encourage the reader study this valuable and exciting theory.; Superior advanced textbook or monograph for a graduate course or seminars on real analytic functions.; New to the second edition a revised and comprehensive treatment of the Faá de Bruno formula, topologies on the space of real analytic functions,; alternative characterizations of real analytic functions, surjectivity of partial differential operators, And the Weierstrass preparation theorem.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 209
• Erscheinungstermin: 8. September 2012
• Englisch
• ISBN-13: 9780817681340
• Artikelnr.: 44203604

Autorenporträt

Krantz, S., Washington University, St.Louis, USA / Parks, H.R., Oregon State University, Corvallis, USA

Inhaltsangabe

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.

Rezensionen

"This is the second, improved edition of the only existing monograph devoted to real-analytic functions, whose theory is rightly considered in the preface 'the wellspring of mathematical analysis.' Organized in six parts, [with] a very rich bibliography and an index, this book is both a map of the subject and its history. Proceeding from the most elementary to the most advanced aspects, it is useful for both beginners and advanced researchers. Names such as Cauchy-Kowalewsky (Kovalevskaya), Weierstrass, Borel, Hadamard, Puiseux, Pringsheim, Besicovitch, Bernstein, Denjoy-Carleman, Paley-Wiener, Whitney, Gevrey, Lojasiewicz, Grauert and many others are involved either by their results or by their concepts." -MATHEMATICAL REVIEWS "Bringing together results scattered in various journals or books and presenting them in a clear and systematic manner, the book is of interest first of all for analysts, but also for applied mathematicians and researchers in real algebraic geometry." -ACTA APPLICANDAE MATHEMATICAE