Generalized Function - Topological Groups

Topological Groups

Bruhat introduced a class of test functions, the Schwartz–Bruhat functions as they are now known, on a class of locally compact groups that goes beyond the manifolds that are the typical function domains. The applications are mostly in number theory, particularly to adelic algebraic groups. André Weil rewrote Tate's thesis in this language, characterizing the zeta distribution on the idele group; and has also applied it to the explicit formula of an L-function.