Dual integral equations with trigonometrical kernels

Abstract

In the analysis of mixed boundary value problems in the plane, we encounter dual integral equations of the typeIf 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.