The $$\mathcal {F}$$-Resolvent Equation and Riesz Projectors for the $$\mathcal {F}$$-Functional Calculus

Abstract The Fueter-Sce-Qian mapping theorem gives a constructive way to extend holomorphic functions of one complex variable slice hyperholomorphic functions. By means the Cauchy formula for it is possible have in integral form n odd. On this based $$ \mathcal {F}$$ F -functional calculus -tuples commuting operators. It functional on commutative version S spectrum. Furthermore, monogenic spirit McIntosh and collaborators. In paper, inspired by quaternionic case some particular Clifford algebras cases, we show general resolvent equation algebra setting. Moreover, prove that -resolvent suitable study Riesz projectors.