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.
A Primer of Real Analytic Functions
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"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
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Inside This Book
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First Sentence:
We begin with power series on the real line R. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
real analytic inverse function theorem, semianalytic subset, real analytic submanifold, subanalytic subset, real analytic functions, real analytic category, real analytic coefficients, convex sequence, real analytic manifold, several real variables, real analyticity, uniformization theorem, preparation theorem, analytic manifolds, derived series, limit topology, power series converges, implicit function theorem, embedding problem, normal bundle, tempered distribution, symmetric body Key Phrases - Capitalized Phrases (CAPs): (learn more)
Abel's Lemma, The Embedding of Real Analytic Manifolds, Hassler Whitney New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We begin with power series on the real line R. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
real analytic inverse function theorem, semianalytic subset, real analytic submanifold, subanalytic subset, real analytic functions, real analytic category, real analytic coefficients, convex sequence, real analytic manifold, several real variables, real analyticity, uniformization theorem, preparation theorem, analytic manifolds, derived series, limit topology, power series converges, implicit function theorem, embedding problem, normal bundle, tempered distribution, symmetric body Key Phrases - Capitalized Phrases (CAPs): (learn more)
Abel's Lemma, The Embedding of Real Analytic Manifolds, Hassler Whitney New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 53
books:
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18
books
cite this book:
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- Complex Analysis (Lecture Notes in Mathematics) by Steven G. Krantz in Back Matter (1), and Back Matter (2)
- The Geometry of Domains in Space (Birkhäuser Advanced Texts Basler Lehrbücher) by Steven G. Krantz in Back Matter (1), and Back Matter (2)
- Differentiable Manifolds by Lawrence Conlon in Back Matter (1), and Back Matter (2)
- Partial Differential Equations (Applied Mathematical Sciences) (v. 1) by Fritz John in Back Matter (1), and Back Matter (2)
- Algebraic Geometry (Dover Books on Mathematics) by Solomon Lefschetz in Front Matter, and Back Matter
See all 53 books this book cites
- Problems in Mathematical Analysis II (Student Mathematical Library, Vol. 12) by W. J. Kaczor in Front Matter, and Back Matter
- The Geometry of Domains in Space (Birkhäuser Advanced Texts Basler Lehrbücher) by Steven G. Krantz in Back Matter (1), and Back Matter (2)
- Real Analysis by Emmanuele DiBenedetto in Back Matter
- Symplectic Invariants and Hamiltonian Dynamics (Birkhäuser Advanced Texts Basler Lehrbücher) by Helmut Hofer in Back Matter
- Functional Analysis: Spectral Theory (Birkhäuser Advanced Texts Basler Lehrbücher) by V.S. Sunder in Back Matter
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