Spectral dbar equation (${\partial }_{\bar{k}}F(z,k)=S(z,k)$)

A dbar equation in a complex spectral parameter, rather than the original spatial coordinate. In spectral reconstruction, its right-hand side is transformed data. A Cauchy-Pompeiu formula in the spectral plane reconstructs the auxiliary function; an asymptotic coefficient or the original differential equation then recovers the spatial field.