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The solution of a pair of dual integral equations†

Published online by Cambridge University Press:  18 May 2009

M. Lowengrub  and
I. N. Sneddon
M. Lowengrub
Affiliation:
The UniversityGlasgow
I. N. Sneddon
Affiliation:
The UniversityGlasgow
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We define two functions F(p), G(p) in terms of a third function ψ(ζ) by the equations

A standard problem in the theory of dual integral equations is to determine the function ψ(ζ) such that

when the functions f(p), g(p) are prescribed.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 1 , January 1963 , pp. 14 - 18
Copyright
Copyright © Glasgow Mathematical Journal Trust 1963

References

REFERENCES

1Titchmarsh, E. C., Introduction to the theory of Fourier integrals (Clarendon Press, Oxford, 1937), 334–339.Google Scholar
2Busbridge, I. W., Dual integral equations, Proc. London Math. Soc. 44 (1938), 115–129.CrossRefGoogle Scholar
3Gordon, A. N., Dual integral equations, J. London Math. Soc. 29 (1954), 360–363.CrossRefGoogle Scholar
4Copson, E. T., On certain dual integral equations, Proc. Glasgow Math. Assoc. 5 (1961), 21–24.Google Scholar
5Sneddon, I. N., The elementary solution of dual integral equations, Proc. Glasgow Math. Assoc. 4 (1960), 108–110.CrossRefGoogle Scholar
6Tranter, C. J., On some dual integral equations, Quart. J. Math. Oxford Ser. (2) 2 (1951), 60–66.Google Scholar
7Noble, B., Certain dual integral equations, J. Math. Phys. 37 (1958), 128–136.CrossRefGoogle Scholar
8Williams, W. E., The solution of certain dual integral equations, Proc. Edinburgh Math. Soc. 12 (1961), 213–216.CrossRefGoogle Scholar
9Lowengrub, M. and Sneddon, I. N., An axisymmetric boundary value problem of mixed type for a half-space, Proc. Edinburgh Math. Soc. 13 (1962), 39–46.CrossRefGoogle Scholar
10Watson, G. N., A treatise on the theory of Bessel functions (University Press, Cambridge, 1944).Google Scholar
11Whittaker, E. T. and Watson, G. N., A course of modern analysis (University Press, Cambridge, 1920).Google Scholar