A+ CATEGORY SCIENTIFIC UNIT

Function theory in sectors

Volume 163 / 2004

Brian Jefferies Studia Mathematica 163 (2004), 257-287 MSC: Primary 47A60, 46H30; Secondary 47A25, 30G35. DOI: 10.4064/sm163-3-4

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 ${{\mathbb R}}^{n+1}$.

Authors

  • Brian JefferiesSchool of Mathematics
    The University of New South Wales
    Sydney, NSW 2052, Australia
    e-mail

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