The theory and applications of singular integral equations.

The theory of one-dimensional singular integral equations with Cauchy type kernels has been used to great advantage in recent years, in solving many problems encountered in the various branches of Mathematical Physics such as elasticity and fluid mechanics. The fundamentals of the theory appeared independently in papers by H. Poincare and D. Hilbert shortly after the development of the theory of Fredholm equations: Hilbert was working on boundary problems in the theory of analytic functions, while Poincaré was studying the general theory of tides. Although the problems mentioned above often reduced to singular equations of this type, the theory remained undeveloped for some time and the solutions which were obtained by ordinary procedures were mainly unsatisfactory