Quaternionic ψ-hyperholomorphic functions, singular integral operators and boundary value problems II. algebras of singular lntegral operators and riemann type boundary value problems

Abstract

We study some algebras generated by the singular integral operator with the quaternionic Cauchy kernel and the multiplication operators by continuous or piece-wise continuous functions. This allows us to describe the Fredholm theory of hyperholomorphic Riemann boundary value problems whose formulations take into account both the non-commutativity of the quaternionic multiplication and the existence of various classes of hyperholomorphic functions. Certain classes of hyperholomorphic Toenlitz operators are also studied.