One-Dimensional Degenerate Diffusion Operators

The aim of this paper is to present some results about generation, sectoriality and gradient estimates both for the semigroup and for the resolvent of suitable realizations of the operators $A^{\gamma,b}u(x) = \gamma xu''(x) + bu'(x)$, with constants $ \gamma > 0$ and $ b\geq 0$, in the space $C([0,\infty])$