Monogenic Calculus as an Intertwining Operator
Functional Analysis
2007-05-23 v1 Complex Variables
Spectral Theory
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. Keywords: Functional calculus, spectrum, intertwining operator, spectral mapping theorem, jet spaces, monogenic function, Clifford algebra
Cite
@article{arxiv.math/0311285,
title = {Monogenic Calculus as an Intertwining Operator},
author = {Vladimir V. Kisil},
journal= {arXiv preprint arXiv:math/0311285},
year = {2007}
}
Comments
16 pages, 3 PS figures