I have the convolution of two non-periodic, continuous and differentiable functions $f(t)$ and $g(t)$ is a constant $K \in \mathbb{R}$, i.e., $(f∗g)(t)=K \quad \forall t \in \mathbb{R}$.

Can I conclude that $f$ or $g$ must be a constant? I need to mention that we know $f$ has Fourier Transform but we do not know $g$ has Fourier Transform or not!

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    $\begingroup$ How do you know that the convolution is well defined? $\endgroup$ – copper.hat Dec 14 '16 at 16:31
  • $\begingroup$ Actually it is an equation I need to solve, resulting from KTC conditions. $\endgroup$ – Mohammad Dec 14 '16 at 16:34

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