Function theory in sectors

Brian Jefferies¹

¹ School of Mathematics The University of New South Wales Sydney, NSW 2052, Australia

Studia Mathematica, Tome 163 (2004) no. 3, pp. 257-287

Résumé

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

Détail

DOI : 10.4064/sm163-3-4

Keywords: shown there one to one correspondence between uniformly bounded holomorphic functions complex variables sectors mathbb uniformly bounded functions real variables sectors mathbb monogenic functions sense clifford analysis result applied construction functional calculi commuting operators including example differentiation operators lipschitz surface mathbb