Monogenic Calculus as an Intertwining Operator

2003/11/17 by Vladimir V. Kisil
Mathematics · #math.FA #math.CV #math.SP #msc:47A60 #msc:30G35 #msc:46H30 #msc:47A10 #msc:47B15

paper · pdf

published as Bull. Belg. Math. Soc. Simon Stevin, 11(2005), no.5, pp.739--757 · 16 pages, 3 PS figures

arxiv created 2003/11/17 · arxiv updated 2009/12/01

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

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