Explicit error terms for asymptotic expansions of Mellin convolutions

DOI10.1016/0022-247X(79)90261-0zbMath0431.44003OpenAlexW2106341564MaRDI QIDQ1138183

Roderick Wong

Publication date: 1979

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

Full work available at URL: https://doi.org/10.1016/0022-247x(79)90261-0

zbMATH Keywords

Fourier transformsasymptotic expansionsHilbert transformsoscillatory kernelsMellin convolutiongeneralized Stieltjes transformspotential transforms

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Asymptotics of solutions to integral equations (45M05)

Related Items (20)

Regular singular asymptotics ⋮ Asymptotic Expansions of Generalized Stieltjes Transforms of Algebraically Decaying Functions ⋮ On an Asymptotic Expansion of the Kontorovich–Lebedev Transform ⋮ Asymptotic expansions of Mellin convolutions by means of analytic continuation ⋮ Finite-part integration of the generalized Stieltjes transform and its dominant asymptotic behavior for small values of the parameter. I. Integer orders ⋮ Asymptotic evaluation of integrals involving multiple scales ⋮ Asymptotic Expansions of Some Integral Transforms by Using Generalized Functions ⋮ On a modification of Wong´s asymptotic expansion of the Kontorovich–Lebedev transform ⋮ Unnamed Item ⋮ The resolvent and the heat kernel for some singular boundary problems ⋮ Computation of Mellin convolution integrals with a logarithmic kernel: application to the third Appell function ⋮ The resolvent expansion for second order regular singular operators ⋮ Symmetric standard elliptic integrals with two or three large parameters ⋮ Moment Asymptotic Expansions of the Wavelet Transforms ⋮ Asymptotic expansions of the Mehler-Fock transform ⋮ Asymptotic expansions of the wavelet transform for large and small values of \(b\) ⋮ Asymptotic expansions of mellin convolution integrals: an oscillatory case ⋮ Integrals with a large parameter: Hilbert transforms ⋮ Asymptotic expansions of the kontorovich—lebedev transform ⋮ An Asymptotic Expansion of Continuous Wavelet Transform for Small Dilation Parameter

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Slowly varying functions and asymptotic behavior of a class of integral transforms. I
• Inversion of a convolution transform by use of series
• Asymptotic expansion of a class of integral transforms with algebraically dominated kernels
• Exact Remainders for Asymptotic Expansions of Fractional Integrals
• Asymptotic Expansion of the Hilbert Transform
• Error Bounds for Asymptotic Expansions of Hankel Transforms
• Explicit Error Terms for Asymptotic Expansions of Stieltjes Transforms
• Asymptotic Expansion of Laplace Transforms Near the Origin
• Error Bounds for Stationary Phase Approximations

This page was built for publication: Explicit error terms for asymptotic expansions of Mellin convolutions