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Nunes, Jos\\'e Mour\\~ao, Pei Dang, Tao Qian","submitted_at":"2016-12-05T11:50:22Z","abstract_excerpt":"We introduce a one-parameter family of transforms, $U^t_{(m)}$, $t>0$, from the Hilbert space of Clifford algebra valued square integrable functions on the $m$--dimensional sphere, $L^2(S^{m},d\\sigma_{m})\\otimes \\mathbb{C}_{m+1}$, to the Hilbert spaces, ${\\mathcal M}L^2(\\mathbb{R}^{m+1} \\setminus \\{0\\},d\\mu_t)$, of monogenic functions on $\\mathbb{R}^{m+1}\\setminus \\{0\\}$ which are square integrable with respect to appropriate measures, $d\\mu_t$. 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