Nonlinear conditions for ultradifferentiability: a uniform approach (Q2120882)

Joris's theorem states that a function \(f\) is smooth if its two consecutive powers are smooth. In the paper, the authors give a uniform proof of this statement to be valid for all ultradifferentiable classes \({\mathcal C}\) and in all dimension. Using the proposed method, the result can be proved for infinite-dimensional Banach spaces and convenient vector spaces.