Abstract
The major difficulty in using the Wiener-Hopf technique is the problem of constructing a suitable factorization. We consider here a method based on contour integration which leads by natural extensions to the use of Cauchy integrals in the solution of mixed boundary-value problems.
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Footnotes
See NOBLE (1958), p. 93ff. for details.
C. Mark, Phys. Rev. (1947), 72, 558; G. Placzek, Phys. Rev. (1947), 72, 556.
MUSKHELISHVILI (1953).
We could in fact use a Fourier inversion contour which is not a straight line parallel to the real axis, thus achieving a generalization of the Wiener-Hopf technique by using the Plemelj formula.
MUSKHELISHVILI (1953), Ch. 2.
MUSKHELISHVILI (1953), Ch. 4.
We could in fact use a Fourier inversion contour which is not a straight line parallel to the real axis, thus achieving a generalization of the Wiener-Hopf technique by using the Plemelj formula.
Based on work by K. M. Case and R. D. Hazeltine, J. Math. Phys. (1971), 12, 1970.
See CASE $ ZWEIFEL (1967) for the derivation and inter- pretation of this equation.
Proved in CASE & ZWEIFEL (1967), p. 62 ff.
See ref. 8 for another example.
Based on a paper by K. M. Case, Rev. Mod. Phys. (1964), 36, 669.
See Section 10.4.
The techniques used for the solution of these singular integral equations are quite standard; see MUSKHELISHVILI (1953).
P. Wolfe, SIAM J. Appl. Math. (1972), 23, 118.
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© 1978 Springer Science+Business Media New York
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Davies, B. (1978). Methods Based on Cauchy Integrals. In: Integral Transforms and Their Applications. Applied Mathematical Sciences, vol 25. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-5512-1_19
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DOI: https://doi.org/10.1007/978-1-4757-5512-1_19
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