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The solution of dual series and dual integral equations

Published online by Cambridge University Press:  18 May 2009

W. E. Williams
W. E. Williams
Affiliation:
The University Liverpool
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There exist several different approaches to the problem of solving dual integral equations involving Bessel Functions [1, 2, 3, 4, 5, 6,7], and Erdelyi and Sneddon in a recent paper [8] have shown that the introduction of certain operators occurring in the theory of fractional integration enables the relationships between the various methods to be clearly demonstrated. For dual integral equations other than those involving Bessel Functions the operators introduced by Erdélyi and Sneddon are not always the appropriate ones to use and it seems to be of interest to consider this more general type of situation.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 3 , January 1964 , pp. 123 - 129
Copyright
Copyright © Glasgow Mathematical Journal Trust 1964

References

REFERENCES

1.Titchmarsh, E. C., Theory of Fourier integrals (Oxford, 1937), p. 334.Google Scholar
2.Busbridge, I. W., Dual integral equations, Proc. London Math. Soc. 44 (1938), 115–129.Google Scholar
3.Gordon, A. N., Dual integral equations, J. London Math. Soc. 29 (1954), 360–363.CrossRefGoogle Scholar
4.Copson, E. T., On certain dual integral equations, Proc. Glasgow Math. Assoc. 5 (1961), 21–24.CrossRefGoogle Scholar
5.Sneddon, I. N., The elementary solution of dual integral equations, Proc. Glasgow Math. Assoc. 4 (1960), 108–110.CrossRefGoogle Scholar
6.Noble, B., Certain dual integral equations, J. Math. Phys. 37 (1955), 128–136.CrossRefGoogle Scholar
7.Williams, W. E., Solution of certain dual integral equations, Proc. Edinburgh Math. Soc. 12 (1961), 213–216.CrossRefGoogle Scholar
8.Erdélyi, A. and Sneddon, I. N., Fractional integration and dual integral equations, Canad. J. Math. 14 (1962), 685–693.Google Scholar
9.Copson, E. T., On the problem of the electrified disc, Proc. Edinburgh Math. Soc. 8 (1947), 14–19.CrossRefGoogle Scholar
10.Tranter, C. J., Dual trigonometrical series, Proc. Glasgow Math. Assoc. 4 (1960), 49–57.CrossRefGoogle Scholar
11.Collins, W. D., On some dual series equations and their applications to electrostatic problems for spheroidal caps, Proc. Cambridge Philos. Soc. 57 (1961), 367–384.CrossRefGoogle Scholar
12.Noble, B., Wiener-Hopf methods (Oxford, 1958), p. 230.Google Scholar
13.Williams, W. E., A class of mixed boundary value problems, J. Math. Mech. 11 (1962), 109–120.Google Scholar
14.Williams, W. E., Diffraction by a disk, Proc. Roy. Soc. Ser. A 267 (1962), 77–87.Google Scholar
15.Williams, W. E., A class of integral equations, Proc. Cambridge Philos. Soc. 59 (1963), 589–597.CrossRefGoogle Scholar
16.Tranter, C. J., On some dual integral equations, Quart. J. Math. Oxford Ser. (2) 2 (1951), 60–66.CrossRefGoogle Scholar
17.Jones, D. S., A new method for calculating scattering with particular reference to the circular disk, Comm. Pure Appl. Math. 9 (1956), 713–746.Google Scholar
18.Sneddon, I. N., Fractional integration and dual integral equations (North Carolina State College, 06 1962).Google Scholar