| Analysis on Real and Complex Manifolds: Volume 35 Revised Edition Contributor(s): Narasimhan, R. (Author) |
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ISBN: 0444877762 ISBN-13: 9780444877765 Publisher: North-Holland OUR PRICE: $163.35 Product Type: Hardcover - Other Formats Published: December 1985 Annotation: Chapter 1 presents theorems on differentiable functions often used in differential topology, such as the implicit function theorem, Sard's theorem and Whitney's approximation theorem. The next chapter is an introduction to real and complex manifolds. It contains an exposition of the theorem of Frobenius, the lemmata of Poincare and Grothendieck with applications of Grothendieck's lemma to complex analysis, the imbedding theorem of Whitney and Thom's transversality theorem. Chapter 3 includes characterizations of linear differentiable operators, due to Peetre and Hormander. The inequalities of Garding and of Friedrichs on elliptic operators are proved and are used to prove the regularity of weak solutions of elliptic equations. The chapter ends with the approximation theorem of Malgrange-Lax and its application to the proof of the Runge theorem on open Riemann surfaces due to Behnke and Stein. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential |
| Dewey: 516.36 |
| LCCN: 85010155 |
| Series: North-Holland Mathematical Library |
| Physical Information: 0.63" H x 6.14" W x 9.21" (1.20 lbs) 245 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Chapter 1 presents theorems on differentiable functions often used in differential topology, such as the implicit function theorem, Sard's theorem and Whitney's approximation theorem. The next chapter is an introduction to real and complex manifolds. It contains an exposition of the theorem of Frobenius, the lemmata of Poincar and Grothendieck with applications of Grothendieck's lemma to complex analysis, the imbedding theorem of Whitney and Thom's transversality theorem. Chapter 3 includes characterizations of linear differentiable operators, due to Peetre and Hormander. The inequalities of Garding and of Friedrichs on elliptic operators are proved and are used to prove the regularity of weak solutions of elliptic equations. The chapter ends with the approximation theorem of Malgrange-Lax and its application to the proof of the Runge theorem on open Riemann surfaces due to Behnke and Stein. |