复八元数分析中的Plemelj公式
Plemelj Formula in Complex Octonionic Analysis
DOI: 10.12677/pm.2026.164088, PDF,    国家自然科学基金支持
作者: 吕嘉珍, 王海燕, 屈非非:天津职业技术师范大学理学院,天津
关键词: 复八元数分析Cauchy积分公式Plemelj公式Complex Octonionic Analysis Cauchy Formula Plemelj Formula
摘要: 复八元数作为八元数在复数域上的推广,在理论物理领域展现出重要应用价值。它能描述量子力学中的自旋态、电磁场的双曲对称性以及角动量算子与力矩张量。本文首先建立了复八元数空间中类似于Hile引理的一种核函数的不等式,随后讨论了Cauchy主值的存在性,最后研究复八元数空间中分片光滑曲面上的Plemelj公式。
Abstract: As an extension of octonions over the complex number field, complex octonions have shown significant application value in theoretical physics. They can describe spin states in quantum mechanics, the hyperbolic symmetry of electromagnetic fields, and angular momentum operators and moment tensors. This paper first establishes an inequality of a kernel function similar to Hile’s lemma in the complex octonionic space. Then, it discusses the existence of the Cauchy principal value. Finally, it studies the Plemelj formula on piecewise smooth surfaces in the complex octonionic space.
文章引用:吕嘉珍, 王海燕, 屈非非. 复八元数分析中的Plemelj公式[J]. 理论数学, 2026, 16(4): 25-35. https://doi.org/10.12677/pm.2026.164088

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