Monogenic plane waves and the \(W\)-functional calculus (Q2786705)

In the setting of Clifford-algebra-valued functions, the Cauchy formula for slice monogenic functions is used to define the known \(S\)-functional calculus. In a similar manner the authors use an integral transform that maps slice monogenic functions into plane waves monogenic functions to develop a functional calculus depending on a parameter which they call \(W\)-functional calculus and which works for \(n\)-tuples of not necessarily commuting operators. Properties of the \(W\)-functional calculus are proved.NEWLINENEWLINE Further, two other integral transforms mapping slice monogenic functions into monogenic functions are suggested as candidates for use in developing other useful forms of functional calculus.