Soit $f$ un morphisme propre et de Nash d’un ouvert $\Omega$ de ${\mathbf{R}}^n$ dans un ouvert ${\Omega }^{\text{'}}$ de ${\mathbf{R}}^p$. Nous démontrons que l’image par $f^{*}$ de l’algèbre $C^{\infty }({\Omega }^{\text{'}})$ des fonctions réelles $C^{\infty }$ dans ${\Omega }^{\text{'}}$ est fermée dans $C\infty \left(\Omega \right)$ munie de sa topologie habituelle d’espace de Fréchet. Ce résultat généralise, dans le cas algébrique, un résultat de G. Glaeser sur les fonctions composées différentiables.

The methodology of fractal interpolation is very useful for processing experimental signals in order to extract their characteristics of complexity. We go further and prove that the Iterated Function System involved may also be used to obtain new approximants that are close to classical ones. In this work a classical function and a fractal function are combined to construct a new interpolant. The fractal function is first defined as a perturbation of a classical mapping. The additional condition...

MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf GorenfloWe generalize the two forms of the fractional derivatives (in Riemann-Liouville and Caputo sense) to spaces of generalized functions using appropriate techniques such as the multiplication of absolutely continuous function by the Heaviside function, and the analytical continuation. As an application, we give the two forms of the fractional derivatives of discontinuous functions in spaces of distributions.