Change of variable formulas for regularizing slowly decaying and oscillatory Cauchy and Hilbert transforms

DOI10.1142/S0219530514500353zbMath1297.30063arXiv1311.2320OpenAlexW2095908810MaRDI QIDQ5170148

Sheehan Olver

Publication date: 18 July 2014

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.2320

zbMATH Keywords

Cauchy integralsingular integral

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20)

Related Items

Applying an iterative method numerically to solve n × n matrix Wiener–Hopf equations with exponential factors ⋮ Critical behavior for scalar nonlinear waves

Uses Software

• DLMF
• OPQ

Cites Work

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• A practical algorithm for computing Cauchy principal value integrals of oscillatory functions
• A general framework for solving Riemann-Hilbert problems numerically
• Computation of equilibrium measures
• Computing the Hilbert transform of a Jacobi weight function
• Two new formulas for the numerical evaluation of the Hilbert transform
• Asymptotic expansions and fast computation of oscillatory Hilbert transforms
• Computing the Hilbert transform and its inverse
• Exponential asymptotics and gravity waves
• Asymptotic Expansion of the Hilbert Transform
• Numerical solution of second-order linear difference equations
• A trigonometric quadrature rule for Cauchy integrals with Jacobi weight

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