Question

A singular integral is the integral that contains

Answer 1

Answer:

An equation containing the unknown function under the integral sign of an improper integral in the sense of Cauchy (cf. Cauchy integral). Depending on the dimension of the manifold over which the integrals are taken, one distinguishes one-dimensional and multi-dimensional singular integral equations. In comparison with the theory of Fredholm equations (cf. Fredholm equation), the theory of singular integral equations is more complex. For example, the theories of one-dimensional and multi-dimensional singular integral equations, both in the formulation of definitive results and in the methods used to establish them, differ significantly from one another. In the one-dimensional case, the theory is more fully developed, and its results are formulated more simply than the corresponding results in the multi-dimensional case. In what follows, main attention will be given to the one-dimensional case.