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Analysis on real and complex manifolds

Author: Raghavan Narasimhan
Publisher: Amsterdam ; New York : North-Holland ; New York, N.Y. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1985, ©1968.
Series: North-Holland mathematical library, v. 35.
Edition/Format:   Print book : EnglishView all editions and formats
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Raghavan Narasimhan
ISBN: 0444877762 9780444877765
OCLC Number: 12049887
Description: xiv, 246 pages ; 23 cm.
Contents: 1. Differentiable Functions in Rn. Taylor's Formula. Partitions of Unity. Inverse Functions, Implicit Functions and the Rank Theorem. Sard's Theorem and Functional Dependence. Borel's Theorem on Taylor Series. Whitney's Approximation Theorem. An Approximation Theorem for Holomorphic Functions. Ordinary Differential Equations. 2. Manifolds. Basic Definitions. The Tangent and Cotangent Bundles. Grassmann Manifolds. Vector Fields and Differential Forms. Submanifolds. Exterior Differentiation. Orientation. Manifolds with Boundary. Integration. One Parameter Groups. The Frobenius Theorem. Almost Complex Manifolds. The Lemmata of Poincare and Grothendieck. Applications: Hartog's Continuation Theorem and the Oka-Weil Theorem. Immersions and Imbeddings: Whitney's Theorems. Thom's Transversality Theorem. 3. Linear Elliptic Differential Operators. Vector Bundles. Fourier Transforms. Linear Differential Operators. The Sobolev Spaces. The Lemmata of Rellich and Sobolev. The Inequalities of Garding and Friedrichs. Elliptic Operators with C Coefficients: The Regularity Theorem. Elliptic Operators with Analytic Coefficients. The Finiteness Theorem. The Approximation Theorem and Its Application to Open Riemann Surfaces
Series Title: North-Holland mathematical library, v. 35.
Responsibility: R. Narasimhan.
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