In this paper we study some problems of the canonical harmonic analysis on the field Qₚ of p -adic numbers. The main elements of the canonical harmonic analysis on Qₚ are canonical Fourier integral transforms, canonical generalized translation operators and canonical convolution products for functions on Qₚ. We consider various results of the canonical harmonic analysis for functions from Lebesgue spaces L^ (Qₚ), 1. Basic concepts of the canonical harmonic analysis on Qₚ are expand to generalized functions (or distributions), among them the canonical Fourier transforms on Qₚ, the generalized translation operators on Qₚ and others. The analogues of various results of classical harmonic analysis, including analogues of the Paley-Wiener-Schwartz theorems, are proved. We introduce a canonical convolution product on Qₚ for usual and generalized functions and establish some of its properties.
С А Платонов (Wed,) studied this question.