The Fourier, Hilbert and Mellin transforms on a half-line

Emilia L. K. Blåsten, Lassi Päivärinta, Sadia Sadique

We are interested in the singular behaviour at the origin of solutions to the equation $\mathcal{H}\rho =e$ on a half-axis, where $\mathcal{H}$ is the one-sided Hilbert transform, $\rho$…