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Abstract

It is shown that there is a one-to-one correspondence between uniformly bounded holomorphic functions of $n$ complex variables in sectors of ${{\mathbb C}}^n$, and uniformly bounded functions of $n+1$ real variables in sectors of ${{\mathbb R}}^{n+1}$ that are monogenic functions in the sense of Clifford analysis. The result is applied to the construction of functional calculi for $n$ commuting operators, including the example of differentiation operators on a Lipschitz surface in ${{\mathbb R}}^{n+1}$.