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

doi:10.1007/s00020-011-1909-9

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 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 language	English
Pages (from-to)	311-326
Number of pages	16
Journal	Integral Equations and Operator Theory
Volume	71
Issue number	3
DOIs	https://doi.org/10.1007/s00020-011-1909-9
State	Published - 1 Nov 2011

Keywords

Clifford and quaternionic analysis
Fueter variables
hyperholomorphic functions
Taylor series

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s00020-011-1909-9

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AU - Luna-Elizarrarás, María Elena

AU - Shapiro, Michael

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 - hyperholomorphic functions

KW - Taylor series

UR - http://www.scopus.com/inward/record.url?scp=80255141855&partnerID=8YFLogxK

U2 - 10.1007/s00020-011-1909-9

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JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 3

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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