The F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {F}$$\end{document}-Resolvent Equation and Riesz Projectors for the F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {F}$$\end{document}-Functional Calculus

The Fueter-Sce-Qian mapping theorem gives a constructive way to extend holomorphic functions of one complex variable to slice hyperholomorphic functions. By means of the Cauchy formula for slice hyperholomorphic functions it is possible to have a Fueter-Sce-Qian mapping theorem in integral form for n odd. On this theorem it is based the F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal {F}$$\end{document}-functional calculus for n-tuples of commuting operators. It is a functional calculus based on the commutative version of the S spectrum. Furthermore, it is a monogenic functional calculus in the spirit of McIntosh and collaborators. In this paper, inspired by the quaternionic case and some particular Clifford algebras cases, we show a general resolvent equation for the F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal {F}$$\end{document}-functional calculus in the Clifford algebra setting. Moreover, we prove that the F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal {F}$$\end{document}-resolvent equation is the suitable equation to study the Riesz projectors.