Asymptotic expansions and fast computation of oscillatory Hilbert transforms

Haiyong Wang, Lun Zhang, Daan Huybrechs

In this paper, we study the asymptotics and fast computation of the one-sided oscillatory Hilbert transforms of the form $$H^{+}(f(t)e^{iωt})(x)=-int_{0}^{\infty}e^{iωt}\frac{f(t)}…