Monogenic Calculus as an Intertwining Operator

Kisil, Vladimir V.

Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, p. 739-757 / Harvested from Project Euclid

Résumé

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.

Publié le : 2005-03-14
Classification: Functional calculus, spectrum, intertwining operator, spectral mapping theorem, jet spaces, monogenic function, Clifford algebra, 47A60, 30G35, 46H30, 47A10, 47B15

@article{1110205630,
     author = {Kisil, Vladimir V.},
     title = {Monogenic Calculus as an Intertwining Operator},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {5},
     year = {2005},
     pages = { 739-757},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1110205630}
}

Kisil, Vladimir V. Monogenic Calculus as an Intertwining Operator. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, pp.  739-757. http://gdmltest.u-ga.fr/item/1110205630/