A Primer of Real Analytic Functions
Springer-Verlag New York Inc.
978-1-4612-6412-5 (ISBN)
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.
"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
Erscheint lt. Verlag | 7.9.2012 |
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Reihe/Serie | Birkhäuser Advanced Texts Basler Lehrbücher |
Zusatzinfo | XIII, 209 p. |
Verlagsort | New York |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 1-4612-6412-X / 146126412X |
ISBN-13 | 978-1-4612-6412-5 / 9781461264125 |
Zustand | Neuware |
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