We are not able to resolve this OAI Identifier to the repository landing page. If you are the repository manager for this record, please head to the Dashboard and adjust the settings.
In this paper, we study the asymptotics and fast computation of the one-sided oscillatory Hilbert transforms of the form
H+(f(t)exp(iωt))(x) = ∫exp(iωt)[f(t)/(t-x)], t=0..∞, ω > 0, x ≧ 0,
where the bar indicates the Cauchy principal value and f is a real-valued function with analytic continuation in the first quadrant, except possibly a branch point of algebraic type at the origin. When x = 0, the integral is interpreted as a Hadamard finite-part integral, provided it is divergent. Asymptotic expansions in inverse powers of ω are derived for each fixed x ≧ 0, which clarify the large ω behavior of this transform. We then present efficient and affordable approaches for numerical evaluation of such oscillatory transforms. Depending on the position of x, we classify our discussion into three regimes, namely, x = O(1) or x ≫ 1, 0 < x ≪ 1 and x = 0. Numerical experiments show that the convergence of the proposed methods greatly improve when the frequency ω increases. Some extensions to oscillatory Hilbert transforms with Bessel oscillators are briefly discussed as well.nrpages: 31status: publishe
Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.