Monogenic Calculus as an Intertwining Operator

Details Monogenic Calculus as an Intertwining Operator Monogenic Calculus as an Intertwining Operator

2003-11-17

arxiv.org/abs/math/0311285v1

Bull. Belg. Math. Soc. Simon Stevin, 11(2005), no.5, pp.739--757

Mathematics

Functional Analysis

16 pages, 3 PS figures

Scientific paper

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

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