CARLEMAN TYPE SINGULAR INTEGRAL EQUATIONS.
We present a consolidated account of Carleman type singular integral equations. We have started from the most basic equation of this type and have at first attempted to integrate from the existing literature the progress which has been made so far in this field. Many different techniques are presented to solve these types of integral equations both in the real and the complex domains. In the complex domain both closed and open contours for integrals are considered. In the process of this study we find that many known methods need to be polished and extended. We attempt to accomplish this and then interrelate different concepts and solutions. Thereby we obtain solutions of more general singular integral equations of the Carleman type. Many interesting examples are presented to illustrate the general theory.
Publication Source (Journal or Book title)
Estrada, R., & Kanwal, R. (1987). CARLEMAN TYPE SINGULAR INTEGRAL EQUATIONS.. SIAM Review, 29 (2), 263-290. https://doi.org/10.1137/1029044