On the Structure of the Taylor Series in Clifford and Quaternionic Analysis

Daniel Alpay, Flor de María Correa-Romero, María Elena Luna-Elizarrarás, Michael Shapiro

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)311-326
Number of pages16
JournalIntegral Equations and Operator Theory
Volume71
Issue number3
DOIs
StatePublished - 1 Nov 2011

Keywords

  • Clifford and quaternionic analysis
  • Fueter variables
  • Taylor series
  • hyperholomorphic functions

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