The operator of inversion as an everywhere continuous nowhere differentiable function
The authors give an interesting survey on smoothness properties of the inversion operator between various spaces of continuously differentiable functions. The behaviour of this operator exhibits many surprises; for example, it is continuous but nowhere differentiable beyong a certain ``critical'' order. This essentially completes and extends previous work of, e.g., K. P. Rybakowski and R. M. Dudley. The authors seem to be unaware, however, of related work by M. Lanza de Cristoforis.
smoothness properties of the inversion operator
spaces of continuously differentiable functions
scientific article; zbMATH DE number 1563151
scientific article