Clifford Algebra-Valued Segal–Bargmann Transform and Taylor Isomorphism

Classical Segal–Bargmann theory studies three Hilbert space unitary isomorphisms that describe the wave-particle duality and configuration space-phase space. In this work, we generalized these concepts to Clifford algebra-valued functions. We establish among of square-integrable functions on $$\mathbb {R}^n$$ with respect a Gaussian measure, monogenic {R}^{n+1}$$ another measure linear functionals symmetric tensor elements .