The operator of inversion as an everywhere continuous nowhere differentiable function (Q1840586)

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.