ABSTRACT
Theory of the Cauchy type integral and singular integral equations (CTISIE) with a complex variable or several complex variables have been established with range in a complex plane C. This chapter explains that the solutions of singular integral equations for two classes on finite dimensional complex manifolds to C are extended to vector-valued cases with range in a complete Hausdorff locally multiplicatively convex algebra E. It presents the stability of solutions in order to lay a foundation of theory of CTISIE and boundary value problems with domains and ranges in infinite dimensional spaces.
