It is shown that there is a one-to-one correspondence between uniformly bounded holomorphic functions of n complex variables in sectors of ℂⁿ, and uniformly bounded functions of n+1 real variables in sectors of 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 .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-3-4,
author = {Brian Jefferies},
title = {Function theory in sectors},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {257-287},
zbl = {1064.47015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-3-4}
}
Brian Jefferies. Function theory in sectors. Studia Mathematica, Tome 162 (2004) pp. 257-287. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-3-4/