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Asymptotic expansions of Fourier transforms of functions with logarithmic singularities. (English) Zbl 0394.42005


MSC:

42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
30E15 Asymptotic representations in the complex plane
45M05 Asymptotics of solutions to integral equations
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References:

[1] Bleistein, N., Asymptotic expansions of integral transforms of functions with logarithmic singularities, SIAM J. Math. Anal., 8, 655-672 (1977) · Zbl 0361.42016
[2] Erdélyi, A., Asymptotic expansions of Fourier integrals involving logarithmic singularities, SIAM J. Appl. Math., 4, 38-47 (1956) · Zbl 0072.11703
[3] Handelsman, R. A.; Lew, J. S., Asymptotic expansion of a class of integral transforms with algebraically dominated kernels, J. Math. Anal. Appl., 35, 405-433 (1971) · Zbl 0214.36702
[4] Lyness, J. N., Adjusted forms of the Fourier coefficient asymptotic expansion and applications in numerical quadrature, Math. Comp., 25, 87-104 (1971) · Zbl 0217.52501
[5] Riekstins, E., Asymptotic expansions for some type of integrals involving logarithms, Latvian Math. Yearbook, 15, 113-130 (1974) · Zbl 0298.41019
[6] Wong, R.; Wyman, M., A generalization of Watson’s lemma, Canad. J. Math., 24, 185-208 (1972) · Zbl 0278.41032
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