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 , so that special methods have to be derived for the solution.
(Received August 26 1961)
† 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.