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Lookup NU author(s): Dr David Kimsey
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© Springer Nature Switzerland AG 2018. 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.
Author(s): Colombo F, Gantner J, Kimsey DP
Publication type: Book Chapter
Publication status: Published
Book Title: Operator Theory: Advances and Applications
Year: 2019
Volume: 270
Pages: 1-10
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_1
DOI: 10.1007/978-3-030-03074-2_1
Library holdings: Search Newcastle University Library for this item
ISBN: 9783030030735