I am only recently familiarizing myself with basic harmonic analysis so pardon me if my question seems odd. I have a locally compact abelian topological group $G$. For $f:G\rightarrow \mathbb{C}$ I have the definition $$f*\mu(x)=\int \Delta(y^{-1})f(xy^{-1})dy$$ And I have the identity $$\int f(x^{-1})\Delta(x^{-1})dx=\int f(x)dx$$ So with these two, wouldn't we get $f*\mu(x)=\int f(xy)dy$ ?
2026-03-27 06:08:56.1774591736
Is $f*\mu(x)=\int f(xy)dy$?
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