Bulletin of the Belgian Mathematical Society - Simon Stevin

Monogenic Calculus as an Intertwining Operator

Vladimir V. Kisil

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Abstract

We revise a monogenic calculus for several non-commuting operators, which is defined through group representations. Instead of an algebraic homomorphism we use group covariance. The related notion of joint spectrum and spectral mapping theorem are discussed. The construction is illustrated by a simple example of calculus and joint spectrum of two non-commuting selfadjoint (n\times n) matrices.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin Volume 11, Number 5 (2005), 739-757.

Dates
First available in Project Euclid: 7 March 2005

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1110205630

Mathematical Reviews number (MathSciNet)
MR2130636

Zentralblatt MATH identifier
1089.47021

Subjects
Primary: 47A60: Functional calculus 30G35: Functions of hypercomplex variables and generalized variables 46H30: Functional calculus in topological algebras [See also 47A60] 47A10: Spectrum, resolvent 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)

Keywords
Functional calculus spectrum intertwining operator spectral mapping theorem jet spaces monogenic function Clifford algebra

Citation

Kisil, Vladimir V. Monogenic Calculus as an Intertwining Operator. Bull. Belg. Math. Soc. Simon Stevin 11 (2005), no. 5, 739--757. https://projecteuclid.org/euclid.bbms/1110205630.


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