Continuity of Convolution of Test Functions on Lie Groups
Continuity of Convolution of Test Functions on Lie Groups
If G is a Lie group, let D(G) be the space of compactly supported smooth functions on G. Consider the bilinear map B : D(G) x D(G) -> D(G), (f,g) |-> f*g which takes a pair of test functions to their convolution. We show that B is continuous if and …