Toward infinite‐dimensional Clifford analysis

Abstract

Clifford analysis is a higher dimensional function theory and a refinement of harmonic analysis. We will extend Clifford analysis to the infinite‐dimensional setting. To do that, we have to introduce infinite‐dimensional Clifford algebras and the infinite‐dimensional Dirac operator. The paper's main result is the Wiener chaos decomposition in Clifford analysis. We apply the decomposition to white noise and Brownian motion.