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The upper half space G = {(x 0,…, x n): x 0 > 0} can be considered as the group generated by dilations and translations on ℝn. This group has a natural unitary representation on L 2(ℝn). Using the continuous wavelet transform, certain Banach and Hilbert spaces of functions monogenic (i.e. solutions of the Cauchy-Riemann operator) on the Poincaré half space are constructed. The Hilbert spaces are linked with the fractional calculus of the Dirac operator on ℝn.
Computational Methods and Function Theory – Springer Journals
Published: Mar 7, 2013
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