Geodesic
Distributions and Mnemofunctions on Adeles. Fourier Transform
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 228-240.

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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. 
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E. M. Radyno; Ya. V. Radyno. Distributions and Mnemofunctions on Adeles. Fourier Transform. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 228-240. http://geodesic.mathdoc.fr/item/TM_2004_245_a22/

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