TY - JOUR
T1 - On the Structure of the Taylor Series in Clifford and Quaternionic Analysis
AU - Alpay, Daniel
AU - de María Correa-Romero, Flor
AU - Luna-Elizarrarás, María Elena
AU - Shapiro, Michael
N1 - Funding Information:
M. E. Luna-Elizarrarás and M. Shapiro have been partially supported by CONACYT projects as well by Instituto Politécnico Nacional in the framework of COFAA and SIP programs.
PY - 2011/11
Y1 - 2011/11
N2 - The Fueter variables form a basis of the space of (quaternionic or Cliffordian) hyperholomorphic homogeneous polynomials of degree one, and their symmetrized products give the respective bases of spaces of hyperholomorphic homogeneous polynomials for any degree k. In the present paper we introduce new bases, i.e., new types of hyperholomorphic variables which lead to the Taylor-type series expansions reflecting the structure of the set of all (quaternionic or Cliffordian algebra-valued) hyperholomorphic functions.
AB - The Fueter variables form a basis of the space of (quaternionic or Cliffordian) hyperholomorphic homogeneous polynomials of degree one, and their symmetrized products give the respective bases of spaces of hyperholomorphic homogeneous polynomials for any degree k. In the present paper we introduce new bases, i.e., new types of hyperholomorphic variables which lead to the Taylor-type series expansions reflecting the structure of the set of all (quaternionic or Cliffordian algebra-valued) hyperholomorphic functions.
KW - Clifford and quaternionic analysis
KW - Fueter variables
KW - Taylor series
KW - hyperholomorphic functions
UR - http://www.scopus.com/inward/record.url?scp=80255141855&partnerID=8YFLogxK
U2 - 10.1007/s00020-011-1909-9
DO - 10.1007/s00020-011-1909-9
M3 - Artículo
SN - 0378-620X
VL - 71
SP - 311
EP - 326
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
IS - 3
ER -