Fractional Powers of the Quaternionic d-Bar Derivative

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2023-11-28 DOI:10.1007/s00006-023-01306-7

Arran Fernandez, Cihan Güder, Walaa Yasin

引用次数: 0

Abstract

This work introduces fractional d-bar derivatives in the setting of quaternionic analysis, by giving meaning to fractional powers of the quaternionic d-bar derivative. The definition is motivated by starting from nth-order d-bar derivatives for \(n\in {\mathbb {N}}\), and further justified by various natural properties such as composition laws and its action on special functions such as Fueter polynomials.

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四元数d-Bar导数的分数次幂

本文通过赋予四元数d-bar导数的分数次幂的意义，在四元数分析的背景下引入了分数阶d-bar导数。这个定义的动机是从\(n\in {\mathbb {N}}\)的n阶d-bar导数开始的，并进一步被各种自然性质所证明，如组合定律及其对特殊函数(如Fueter多项式)的作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.