Distributional Solutions of Singular Integral Equations

In this chapter we study the distributional solutions of singular integral equations. The distributional framework is rather convenient for the study of several singular operators, including the singular integrals that we have studied in the previous chapters. Therefore, the study of singular integral equations in spaces of distributions is a natural and important subject. Interestingly, however, the interpretation of singular integrals at the end-points is not straightforward, and so the study of singular integral equations in spaces of distributions over finite intervals turns out to be somewhat difficult. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.