In order to avoid circular convolution $y(t)$ of two functions say $u(t)$ and $v(t)$ in Fourier transforms, the data length must be at least (length $u(t)$)+length($v(t)$)$-$1. If we are interested in deconvolution using the Fourier transform, which may require division of Fourier transform of $y(t)$ by the Fourier transform of $v(t)$ to obtain $u(t)$, do we need to maintain the same length requirements in a mathematically rigorous sense?
All the papers surveyed so far on deconvolution by Fourier methods in the field of spectroscopy never talk about it or mention the issue of circular convolution. Understandably, they don't care about the edge-effects and experimentally there are always excessive data points near the edges which can be discarded. I wanted to confirm that theoretical requirement of data length for deconvolution (division in the Fourier domain) is the same as convolution or not. Thanks.