2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77153We study a fractional differentiation operator for functions on the conjugate space to an infinite extension of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. In particular, a representation in the form of a hypersingular integral operator is obtained. It is also shown that the corresponding diffusion measure is not absolutely continuous with respect to the Gaussian measure.13 pages, AMS-LaTexFunctional AnalysisNumber TheoryProbabilitytext