Can FFT be adapted for deconvolution of non-periodic functions?

Question

Can a non-periodic function be padded at the boundaries and deconvolved with inverse FFT?

Since a Toeplitz matrix can be embedded in a circulant matrix to perform the deconvolution, is there an analogy with the inverse FFT?

Clarification

Not sure if there are other types of deconvolutions but expressed in the frequency ($\omega$) domain, would be the product of the input function $G$ and response function $F$ to get convolved function $H$,

\begin{equation} G(\omega) = \frac{H(\omega)}{F(\omega)} \end{equation}

It is assumed that $G$ and $F$ are periodic, but I am wondering about the case when they are not.

Answer 1

I believe that this is one of the standard methods, but there are stability issues. Check out the Wikipedia article on Wiener deconvolution.