Functions and Operators in Real, Quaternionic, and Cliffordian Contexts

Florian-Horia Vasilescu ()
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Florian-Horia Vasilescu: University of Lille, Department of Mathematics

A chapter in Multivariable Operator Theory, 2023, pp 833-860 from Springer

Abstract: 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.

Keywords: Real; Hamilton and Clifford algebras; Spectral and Cauchy transformations; Clifford and quaternionic operators; Analytic functional calculus; Primary 47A10; Secondary 47A20; 47A60; 30G35; 15A66 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-50535-5_30

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DOI: 10.1007/978-3-031-50535-5_30

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