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Spectral integrals

Lookup NU author(s): Dr David KimseyORCiD

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Abstract

© Springer Nature Switzerland AG 2018. 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.

Publication metadata

Author(s): Colombo F, Gantner J, Kimsey DP

Publication type: Book Chapter

Publication status: Published

Book Title: Operator Theory: Advances and Applications

Year: 2018

Volume: 270

Pages: 219-231

Online publication date: 05/01/2019

Acceptance date: 02/04/2018

Publisher: Birkhaeuser Verlag AG

URL: https://doi.org/10.1007/978-3-030-03074-2_10

DOI: 10.1007/978-3-030-03074-2_10

Library holdings: Search Newcastle University Library for this item

ISBN: 9783030030735

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