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Dual integral equations with trigonometrical kernels†

Published online by Cambridge University Press:  18 May 2009

Ian N. Sneddon
Ian N. Sneddon
Affiliation:
The University Glasgow
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In the analysis of mixed boundary value problems in the plane, we encounter dual integral equations of the type

If we make the substitutions cos we obtain a pair of dual integral equations of the Titchmarsh type [1, p. 334] with α = − 1, v = − ½ (in Titchmarsh's notation). This is a particular case which is not covered by Busbridge's general solution [2], so that special methods have to be derived for the solution.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 5 , Issue 3 , January 1962 , pp. 147 - 152
Copyright
Copyright © Glasgow Mathematical Journal Trust 1962

References

1.Titchmarsh, E. C., Introduction to the theory of Fourier integrals (Clarendon Press, Oxford, 1937).Google Scholar
2.Busbridge, I. W., Dual integral equations, Proc. London Math. Soc. 44 (1938), 115–129.CrossRefGoogle Scholar
3.Chong, F., Solution by dual integral equations of a plane strain Boussinesq problem for an orthotropic medium, Iowa State Coll. Jour, of Sci. 27 (1953), 321–334.Google Scholar
4.Fredricks, R. W., Solution of a pair of integral equations from electrostatics, Proc. Nat. Acad. Sci. 44 (1958), 309–312.CrossRefGoogle Scholar
5.Watson, G. N., A treatise on the theory of Bessel functions, 2nd edn, (Cambridge Univ. Press, 1944).Google Scholar