Abstract:
A classical theorem of Boman states that a function on an open subset of $\mathbb R^d$ is smooth if and only if it maps smooth curves to smooth curves. There is also an ultradifferentiable version of Boman’s theorem. In this talk I will show that these results persist on closed subsets $X$ of $\mathbb R^d$ whose interior is dense in $X$ and has the uniform cone property. I shall also discuss the case that $X$ is a closed subanalytic set with dense interior. Este seminario es parte de la sesión 98 del Seminario Iberoamericano de Matemáticas. De forma extraordinaria tendrá lugar en la facultad de ciencias de la Universidad de Valladolid.