On Van der Corput-type lemmas for Bessel and Airy transforms and applications

DOI10.1016/j.cam.2018.11.007zbMath1459.65033OpenAlexW2901247685WikidataQ124968953 ScholiaQ124968953MaRDI QIDQ1715808

Shuhuang Xiang

Publication date: 29 January 2019

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2018.11.007

zbMATH Keywords

convergence rateasymptotichighly oscillatory integralBessel transformAiry transform

Mathematics Subject Classification ID

Numerical quadrature and cubature formulas (65D32) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Discrete operational calculus (44A55)

Related Items (9)

Interpolation based formulation of the oscillatory finite Hilbert transforms ⋮ Multidimensional van der Corput-type estimates involving Mittag-Leffler functions ⋮ Error estimates of piecewise Hermite collocation method for highly oscillatory Volterra integral equation with Bessel kernel ⋮ Optimal decay rates on the asymptotics of orthogonal polynomial expansions for functions of limited regularities ⋮ On the approximation of highly oscillatory Volterra integral equations of the first kind via Laplace transform ⋮ On optimal convergence rates of Laguerre polynomial expansions for piecewise functions ⋮ Effective collocation methods to solve Volterra integral equations with weakly singular highly oscillatory Fourier or Airy kernels ⋮ Convergence Rates on Spectral Orthogonal Projection Approximation for Functions of Algebraic and Logarithmatic Regularities ⋮ Approximation of highly oscillatory integrals containing special functions

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