Computational Methods and Function Theory 1 (2001), No. 2, 353--374
Copyright Heldermann Verlag 2001
Jan Cnops
jan.cnops@hogent.be, BME, Hogeschool Gent, Schoonmeersstraat 52, B-9000 Gent, Belgium.
The upper half space $G=\{(x_0,\ldots,x_n):\,x_0>0\}$ can be considered as the group generated by dilations and translations on $\R^n$. This group has a natural unitary representation on $L_2(\R^n)$. Using the continuous wavelet transform, certain Banach and Hilbert spaces of functions monogenic (i.e. solutions of the Cauchy-Riemann operator) on the Poincar\'e half space are constructed. The Hilbert spaces are linked with the fractional calculus of the Dirac operator on $\R^n$.
Keywords: Clifford analysis, wavelet transform, weighted Bergman spaces, invariant Dirac operator.
MSC 2000: 30G35, 42B20.
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