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March 2005 Monogenic Calculus as an Intertwining Operator
Vladimir V. Kisil
Bull. Belg. Math. Soc. Simon Stevin 11(5): 739-757 (March 2005). DOI: 10.36045/bbms/1110205630

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.

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Vladimir V. Kisil. "Monogenic Calculus as an Intertwining Operator." Bull. Belg. Math. Soc. Simon Stevin 11 (5) 739 - 757, March 2005. https://doi.org/10.36045/bbms/1110205630

Information

Published: March 2005
First available in Project Euclid: 7 March 2005

zbMATH: 1089.47021
MathSciNet: MR2130636
Digital Object Identifier: 10.36045/bbms/1110205630

Subjects:
Primary: 30G35‎ , 46H30 , 47A10 , 47A60 , 47B15

Keywords: Clifford algebra , functional calculus , intertwining operator , jet spaces , monogenic function , spectral mapping theorem , spectrum

Rights: Copyright © 2005 The Belgian Mathematical Society

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Vol.11 • No. 5 • March 2005
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