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Convolution of $\mathscr{F}\{ \log \}(x) * \mu$ with compactly supported measure $\mu$
As I read in this post the Fourier transform of $\psi(\lambda) = \log{|\lambda|}$ must be interpreted in distributional sense and it is given by:
$$\mathscr{F}\{\psi\}(x)=-2\pi \gamma \delta(x)-\pi \...