Convergence of Subdivision Schemes and Smoothness of Refinable Functions on p-adic Fields

A systematic and comprehensive study of p-adic refinement equations and subdivision scheme associated with a finitely supported refinement mask are carried out in this paper. The Lq -convergence of the subdivision scheme is characterized in terms of the q-norm joint spectral radii of a collection of operators associated with the refinement mask. Also, the smoothness of complex-valued functions on Qp is investigated.