Abstract:

The Sokhotsky-Plemelj formula with holomorphic kernel on the intersection of two balls in $ {\Bbb C}^n$ has a special form, which is piecewise continuous on the boundary. By using this Sokhotsky-Plemelj formula the authors obtain a special composition formula, and get direct solutions to the characteristic equation of the singular integral equation and the system of the singular integral equations with constant coefficients, and convert the general singular integral equation and the system of the singular integral equations with constant coefficients to a Fredholm type equation and a system of equations which are equivalent to them.

Key words: Intersection of two balls in ${\Bbb C}^n$, Composition formula, Singular integral equation, System of the singular integral equations