A Study of <i>α</i> ‐Hyperholomorphic Functions in the Framework of Clifford Analysis

ABSTRACT This paper explores ‐hyperholomorphic functions in Clifford analysis, which satisfy the equation , where is the Dirac operator in , and . Utilizing endomorphisms on Clifford algebra and the method of normalized function systems with respect to the Dirac operator, we derive a Borel–Pompeiu formula for the operator , construct a transmutation operator for , and establish an Almansi‐type decomposition for solutions of the operator .

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Publication Details

Journal
Mathematical Methods in the Applied Sciences
Published
2025-11-04
DOI
https://doi.org/10.1002/mma.70289
Primary Topic
Algebraic and Geometric Analysis
Type
article
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A Study of α ‐Hyperholomorphic Functions in the Framework of Clifford Analysis

Mathematical Methods in the Applied Sciences
Algebraic and Geometric Analysis
article

A Study of α ‐Hyperholomorphic Functions in the Framework of Clifford Analysis

article en

Abstract

ABSTRACT This paper explores ‐hyperholomorphic functions in Clifford analysis, which satisfy the equation , where is the Dirac operator in , and . Utilizing endomorphisms on Clifford algebra and the method of normalized function systems with respect to the Dirac operator, we derive a Borel–Pompeiu formula for the operator , construct a transmutation operator for , and establish an Almansi‐type decomposition for solutions of the operator .

Mathematical Methods in the Applied SciencesVol. 49(4)
Hanoi University of Science and Technology (VN)
Openalex Percentile: Top 34%
Algebraic and Geometric Analysis
DOISourceOpenAlex
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A Study of <i>α</i> ‐Hyperholomorphic Functions in the Framework of Clifford Analysis · Mathematical Methods in the Applied Sciences (2025) | TGRS Research Map | TGRS