2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71360An umbral calculus over local fields of positive characteristic is developed on the basis of a relation of binomial type satisfied by the Carlitz polynomials. Orthonormal bases in the space of continuous $\mathbb F_q$-linear functions are constructed.18 pages, LaTeX-2eNumber TheoryCombinatorics05A40; 11G09; 11S80; 46S10text