Fueter’s Theorem for One Class of Pseudoanalytic Functions

In this paper, we extend Fueter’s theorem in hypercomplex function theory to encompass a class of pseudoanalytic functions associated with the main Vekua equation. This class includes Duffin’s μ -regular functions as special cases, which correspond to the Yukawa equation. As the parameter μ → 0 , we...

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Bibliographic Details
Published in:Advances in applied Clifford algebras 2024-11, Vol.34 (5), Article 57
Main Authors: Han, Yuanyuan, Lian, Pan
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Theorems
Theoretical
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Summary:In this paper, we extend Fueter’s theorem in hypercomplex function theory to encompass a class of pseudoanalytic functions associated with the main Vekua equation. This class includes Duffin’s μ -regular functions as special cases, which correspond to the Yukawa equation. As the parameter μ → 0 , we recover the classical Fueter’s theorem.
ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-024-01361-8