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Differentiable functions. (English) Zbl 0584.58006

From the text: ”This article, based on lectures given at the Instituto de Matemática Pura e Aplicada in 1979, is an introduction to some problems in ’ideals of differentiable functions’ or ’differential analysis’. The problems are local questions in real analysis, focussing, in particular, on the relationships among differential functions, analytic functions and formal power series. The paper includes an exposition (with complete proofs) of some of the fundamental classical theorems, and a discussion of recent results and several important open problems.” Contents: 1. Introduction; 2. Whitney’s extension theorem; 3. The linear structure of ideals of differentiable functions; 4. Composition of differentiable mappings; 5. The Malgrange-Mather division theorem; 6. Resolution of singularities; References.
Reviewer: J.Davidov

MSC:

58C25 Differentiable maps on manifolds
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