Asymptotic Expansion of the Hilbert Transform

DOI10.1137/0511007zbMath0431.44002OpenAlexW2102011800MaRDI QIDQ3868275

Roderick Wong

Publication date: 1980

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0511007

zbMATH Keywords

Hilbert transformasymptotic expansionserror termsrealistic error bounds

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60)

Related Items (10)

High- and low-frequency asymptotic consequences of the Kramers-Kronig relations ⋮ Explicit error terms for asymptotic expansions of Mellin convolutions ⋮ Numerical approximations of highly oscillatory Hilbert transforms ⋮ Asymptotic expansions and fast computation of oscillatory Hilbert transforms ⋮ Double-knife edge problems with elastic/plastic type screens ⋮ A Surprising Observation in the Quarter-Plane Diffraction Problem ⋮ Computing the Hilbert transform and its inverse ⋮ Change of variable formulas for regularizing slowly decaying and oscillatory Cauchy and Hilbert transforms ⋮ The Sommerfeld problem revisited: Solution spaces and the edge conditions ⋮ Integrals with a large parameter: Hilbert transforms

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