In this chapter, we define spectral integrals in the quaternionic setting. The aim is to de_ne them for a suitably large class of functions that allows us to prove the spectral theorem for unbounded operators in Section 12. To this end, we adapt part of Chapter 4 of the book  to the quaternionic setting. Most of the proofs of the properties of spectral integrals are easily adapted from the classical case presented in , i.e., when H is a complex Hilbert space. However, some facts require additional arguments, which we will highlight.
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