Applications of $\mathbf P$-adic generalized functions and approximations by a system of $\mathbf P$-adic translations of a function

Under some conditions we prove that the convergence of a sequence of functions in the space of $\mathbf P$-adic generalized functions is equivalent to its convergence in the space of locally integrable functions. Some analogs are established of the Wiener tauberian theorem and the Wiener theorem on denseness of translations for $\mathbf P$-adic convolutions and translations.