Computational Methods and Function Theory 9 (2009), No. 2, 365--377
Copyright Heldermann Verlag 2009
Yafang Gong
yfgong.math@whu.edu.cn , Wuhan University, School of Mathematics and Statistics, Wuhan, 430072, P. R. China.
Clifford-Hermite Continuous Wavelet Transforms are used to construct a new kind of functional calculus for bounded non-commuting operators. The Weyl calculus can be reobtained from this model. The correspondences between Clifford-Hermite wavelets and functional calculi of operators are discussed in order to obtain operator-valued kernel functions. The functional calculi are then constructed by means of the reconstruction formulae.
Keywords: Clifford-Hermite polynomial, Clifford-Hermite continuous wavelet transform, functional calculus, Weyl calculus.
MSC 2000: 47A60, 46H30, 30G35.
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