Distributions on adeles (Q941957)

The paper is a brief survey of analysis on the adele ring. The authors begin with the basic notions of harmonic analysis on a field \(\mathbb Q_p\) of \(p\)-adic numbers, and then explain how these notions are ``glued together'' in analysis on adeles. The Bruhat-Schwartz spaces of test functions and distributions are considered. See also [\textit{Ya. M. Radyno, Ya. V. Radyno}, Proc. Steklov Inst. Math. 245, 215--227 (2004); translation from Tr. Mat. Inst. Steklova 245, 228--240 (2004; Zbl 1098.11057)].