Approximation of Continuously Differentiable Functions


  • J.G. Llavona

This self-contained book brings together the important results of a rapidly growing area.As a starting point it presents the classic results of the theory. The book covers such results as: the extension of Wells' theorem and Aron's theorem for the fine topology of order m; extension of Bernstein's and Weierstrass' theorems for infinite dimensional Banach spaces; extension of Nachbin's and Whitney's theorem for infinite dimensional Banach spaces; automatic continuity of homomorphisms in algebras of continuously differentiable functions, etc.
View full description


Book information

  • Published: November 1986
  • Imprint: NORTH-HOLLAND
  • ISBN: 978-0-444-70128-2

Table of Contents

Preliminary Results. Approximation of Smooth Functions on Manifolds. Simultaneous Approximation of Smooth Functions. Polynomial Approximation of Differentiable Functions. Weakly Continuous Functions on Banach Spaces. Approximation of Weakly Uniformly Differentiable Functions. Approximation for the Compact-Open Topology. Approximation of Weakly Differentiable Functions. Spaces of Differentiable Functions and the Approximation Property. Polynomial Algebras of Continuously Differentiable Functions. On the Closure of Modules of Continuously Differentiable Functions. Homomorphisms Between Algebras of Uniformly Weakly Differentiable Functions. The Paley-Wiener-Schwartz Theorem in Infinite Dimension. Appendix I: Whitney's Spectral Theorem. References. Index.