Given two functions $f=f(x)$ and $g=g(x)$ and a constant $a$, we all know from the associativity property that $$a(f\ast g)(x)=((af) \ast g)(x)$$ Let's assume that $a=a(x)$, then I would like to determine the following equality $$a(f\ast g)(x)=g(\tilde{f}\ast a)(x)$$ but $\tilde{f}$ is unknown. Is there a way to determine $\tilde{f}$?

I've seen somewhere that $\tilde{f} = \overline{f(-x)}$ but the source is not reliable and the proof is not given.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.