Abstract
This is an expository paper mainly based on certain works due to the author himself. After some introductory sections, we discuss the transformation of vector valued stem functions, defined on sets in the complex plane into quaternionic and Cliffordian valued function, using functional calculi, algebraically or derived via a Cauchy type kernel. Then we consider large families of quaternionic and Cliffordian linear operators, regarded as special classes of real linear operators, extended via a complexification procedure, and thus having the spectrum in the complex plane, which permits the construction of functional calculi with adequate analytic functions, in a classical manner, recaptured by restriction.
Dedicated to the memory of Jörg Eschmeier.
Communicated by Mihai Putinar.
This article is part of the topical collection “Multivariable Operator Theory. The Jörg Eschmeier Memorial” edited by Raul Curto, Michael Hartz, Mihai Putinar and Ernst Albrecht.
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Keywords
- Real
- Hamilton and Clifford algebras
- Spectral and Cauchy transformations
- Clifford and quaternionic operators
- Analytic functional calculus
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© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
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Vasilescu, FH. (2023). Functions and Operators in Real, Quaternionic, and Cliffordian Contexts. In: Albrecht, E., Curto, R., Hartz, M., Putinar, M. (eds) Multivariable Operator Theory. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-50535-5_30
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DOI: https://doi.org/10.1007/978-3-031-50535-5_30
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-031-50534-8
Online ISBN: 978-3-031-50535-5
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