# Introduction

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## Abstract

Since the discovery of the *S*-spectrum in 2006 the theory of slice hyperholomorphic functions has become the underlining function theory on which new functional calculi for quaternionic operators and for *n*-tuples of operators have been developed. These calculi are the *S*-functional calculus and the *F*-functional calculus, and both are based on the notion of *S*-spectrum. In 2014 it was proved that the quaternionic spectral theorem is also naturally based on the *S*-spectrum. These facts restore the analogy with the classical case in which the holomorphic functional calculus and the spectral theorem are based on the same notion of spectrum.

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