Covariant Functional Calculi from the Affine Groups
Gong, Yafang
Bull. Belg. Math. Soc. Simon Stevin, Volume 16 (2009) no. 1, p. 447-461 / Harvested from Project Euclid
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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".
Published online : 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, Volume 16 (2009) no. 1, pp.  447-461. http://gdmltest.u-ga.fr/item/1251832371/