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:
We thank V. Springel for making both GADGET and his galaxy initial condition generator available, and for useful discussions; A.-K. Jappsen for participating in the implementation of sink particles in GADGET; and F. Adams, J. Dalcanton, R. Kennicutt, J. Lee, C. Martin, D. McCray, T. Quinn, M. Shara, and J. van Gorkom for useful discussions. The referee, F. Gov-ernato, also gave valuable comments. This work was supported by NSF grants AST99-85392 and AST03-07854, NASA grant NAG5-13028, and DFG Emmy Noether grant KL1358/1. Computations were performed at the Pittsburgh Supercomputer Center, supported by the NSF, on the Parallel Computing Facility of the AMNH, and on an Ultrasparc III cluster generously donated by Sun Microsystems.

PY - 2011/11/1

Y1 - 2011/11/1

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 - Article

AN - SCOPUS:80255141855

VL - 71

SP - 311

EP - 326

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 3

ER -