A brief note about iterates of derivatives in \(C[0,1]\) and other spaces (Q2419688)

The aim of the present work is to prove the following result: there is a single analytic function \(f\) whose itinerary of derivatives, \(\{f^{(n)}:n\in \mathbb{N}\}\) is dense in \(C[0,1]\). The proof is based on the Weierstrass-Stone theorem and iterated function techniques. An application of the obtained result to the spaces \({{L}^{p}}[0,1]\) is given, too.