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math.CA2011
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)}…
math.NA2011★ 3 cited
On the resolution power of Fourier extensions for oscillatory functions
Ben Adcock, Daan Huybrechs
Functions that are smooth but non-periodic on a certain interval possess Fourier series that lack uniform convergence and suffer from the Gibbs phenomenon. However, they can be rep…