A functional calculus for \(n\)-tuples of noncommuting operators (Q833065)

In the paper under review, the authors give an overview of a new functional calculus for \(n\)-tuples of operators on the basis of the theory of slice monogetic functions with values in a Clifford algebra. Firstly, they prove a couple of technical results useful to define the so-called Cauchy kernel function. Secondly, they introduce the notion of the \(S\)-resolvent operator, the \(S\)-spectrum, the \(S\)-resolvent equation, and then develop a new functional calculus for bounded operators which is consistent with the Riesz-Dunford calculus for a single operator. Finally, the authors consider the cases of unbounded operators.