LAUSR

Classical Segal-Bargmann theory studies three Hilbert space unitary isomorphisms that describe the wave-particle duality and the configuration space-phase space. In this work, we generalized these concepts to Clifford algebra-valued functions. We establish the unitary isomorphisms among the space of Clifford algebra-valued square-integrable functions on Rn with respect to a Gaussian measure, the space of monogenic square-integrable functions on R with respect to another Gaussian measure and the space of Clifford algebra-valued linear functionals on symmetric tensor elements of Rn. Mathematics Subject Classification (2010). Primary 15A66; Secondary 32A36.