Abstract
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 [191] to the quaternionic setting. Most of the proofs of the properties of spectral integrals are easily adapted from the classical case presented in [191], i.e., when H is a complex Hilbert space. However, some facts require additional arguments, which we will highlight.
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Colombo, F., Gantner, J., Kimsey, D.P. (2018). Spectral Integrals. In: Spectral Theory on the S-Spectrum for Quaternionic Operators. Operator Theory: Advances and Applications, vol 270. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-03074-2_10
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DOI: https://doi.org/10.1007/978-3-030-03074-2_10
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-03073-5
Online ISBN: 978-3-030-03074-2
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