Invoking the Clifford-Hermite Wavelets from Clifford analysis,
we use the covariances of affine groups to
construct a kind of functional calculi for several non-commuting
bounded operators. Functional calculi are the intertwining transforms between the
representations of affine groups in the space $L^2(\mathbb R^m)$ and in the
space of bounded operators. It turns out that the Weyl calculus is the value of this new
functional calculus at the identity of affine groups. Our approach is inspired by the mathematical ideas
contained in the paper ``V. V. Kisil.
Wavelets in Banach spaces. Acta Appl. Math. 1999, {\bf 59}(1): 79-109".
Publié le : 2009-08-15
Classification:
Clifford-Hermite Wavelet,
Clifford analysis,
Group covariance,
Affine group,
Weyl calculus,
43A32,
47A60,
47A67,
47L55
@article{1251832371,
author = {Gong, Yafang},
title = {Covariant Functional Calculi from the Affine Groups},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {16},
number = {1},
year = {2009},
pages = { 447-461},
language = {en},
url = {http://dml.mathdoc.fr/item/1251832371}
}
Gong, Yafang. Covariant Functional Calculi from the Affine Groups. Bull. Belg. Math. Soc. Simon Stevin, Tome 16 (2009) no. 1, pp. 447-461. http://gdmltest.u-ga.fr/item/1251832371/