L1 convolution algebra
= L1 convolution algebra
{c}
{title2=$(L^1(G),*)$}
= L1 group algebra
{c}
{synonym}
With left <Haar measure>, $(f*g)(x)=\int_G f(y)g(y^{-1}x)\,dm(y)$ makes $L^1(G)$ a <Banach algebra>, since $\|f*g\|_1\leq\|f\|_1\|g\|_1$. For an Abelian group it is commutative, and the involution is $f^*(x)=\overline{f(x^{-1})}$. Its nonzero <characters of an algebra> are exactly integration against inverses of continuous unitary group characters.
// Target: geometry-and-topology.bigb