Function theory in sectors

Brian Jefferies. "Function theory in sectors." Studia Mathematica 163.3 (2004): 257-287. <http://eudml.org/doc/284980>.

@article{BrianJefferies2004,
abstract = {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 $ℝ^\{n+1\}$ 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 $ℝ^\{n+1\}$.},
author = {Brian Jefferies},
journal = {Studia Mathematica},
keywords = {Clifford algebra; monogenic function; holomorphic function; functional calculus},
language = {eng},
number = {3},
pages = {257-287},
title = {Function theory in sectors},
url = {http://eudml.org/doc/284980},
volume = {163},
year = {2004},
}

TY - JOUR
AU - Brian Jefferies
TI - Function theory in sectors
JO - Studia Mathematica
PY - 2004
VL - 163
IS - 3
SP - 257
EP - 287
AB - 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 $ℝ^{n+1}$ 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 $ℝ^{n+1}$.
LA - eng
KW - Clifford algebra; monogenic function; holomorphic function; functional calculus
UR - http://eudml.org/doc/284980
ER -