Functions and operators in real, quaternionic, ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
Functions and operators in real, quaternionic, and cliffordian contexts
Author(s) :
Journal title :
Complex Analysis and Operator Theory
Publisher :
Springer Verlag
Publication date :
2022-11-05
ISSN :
1661-8254
English keyword(s) :
Real
Hamilton and Clifford algebras
Spectral and Cauchy transformations
Clifford and quaternionic operators
Analytic functional calculus.
Hamilton and Clifford algebras
Spectral and Cauchy transformations
Clifford and quaternionic operators
Analytic functional calculus.
HAL domain(s) :
Mathématiques [math]
English abstract : [en]
This is an expository paper mainly based on certain works due to theauthor himself. After some introductory sections, we discuss the transformation of vector valued stem functions, defined on sets in the complex plane into ...
Show more >This is an expository paper mainly based on certain works due to theauthor 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. Thenwe consider large families of quaternionic and Cliffordian linear operators, regarded as special classes of real linear operators, extended via acomplexification procedure, and thus having the spectrum in the complexplane, which permits the construction of functional calculi with adequateanalytic functions, in a classical manner, recaptured by restriction.Show less >
Show more >This is an expository paper mainly based on certain works due to theauthor 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. Thenwe consider large families of quaternionic and Cliffordian linear operators, regarded as special classes of real linear operators, extended via acomplexification procedure, and thus having the spectrum in the complexplane, which permits the construction of functional calculi with adequateanalytic functions, in a classical manner, recaptured by restriction.Show less >
Language :
Anglais
Popular science :
Non
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