Proceedings of the Glasgow Mathematical Association
- Proceedings of the Glasgow Mathematical Association / Volume 5 / Issue 03 / January 1962, pp 147-152
- Copyright © Glasgow Mathematical Journal Trust 1962
- DOI: http://dx.doi.org/10.1017/S2040618500034481 (About DOI), Published online: 18 May 2009
Research Article
Dual integral equations with trigonometrical kernels†
Ian N. Sneddona1
a1 The University Glasgow
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.
(Received August 26 1961)
Footnotes
† The work described in this paper was done in the the Department of Mathematics, Duke University, North Carolina, and was supported by the U.S. Air Force Office of Scientific Research, A.R.D.C. under contract No. AF 18 (600)–1341. The present paper is a revised version of a part of report AFQSR–TN–60–51 issued by the Department of Mathematics, Duke University.
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