2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58624A number of constructions in function field arithmetic involve extensions from linear objects using digit expansions. This technique is described here as a method of constructing orthonormal bases in spaces of continuous functions. We illustrate several examples of orthonormal bases from this viewpoint, and we also obtain a concrete model for the continuous functions on the integers of a local field as a quotient of a Tate algebra in countably many variables.20 pages, 0 figures, LaTeX, to appear in Journal of Number TheoryNumber Theory11S80;12J25;30G06text