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.
- ISBN10 6612769912
- ISBN13 9786612769917
- Publish Date 15 December 1985 (first published 1 January 1985)
- Publish Status Active
- Out of Print 14 September 2011
- Publish Country US
- Imprint Elsevier Science & Technology
- Format eBook
- Pages 246
- Language English