Distributions and Mnemofunctions on Adeles. Fourier Transform

Some classical results are recalled, and a finite part distribution is interpreted as the zero-order term in the expansion of a homogeneous distribution. An adelic finite part distribution and a generalization of the Tate distribution are defined, and their Fourier transforms are calculated. The machinery of mnemofunctions (nonlinear generalized functions) is adapted to $p$-adic and adelic cases, and product formulas for some specific distributions are given.