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<p>Hypercomplex analysis is the extension of complex analysis to higher dimensions. In its development, besides Clifford analysis, the theory of functions taking values in non-associative Cayley–Dickson algebras has also been considered, especially octonion analysis. In this paper, we construct the Cauchy–Riemann operators in higher-dimensional Cayley–Dickson algebras. We prove the Cauchy integral formula and the Taylor series expansion for solutions of the Cauchy–Riemann operators.</p>

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CAUCHY–RIEMANN OPERATOR IN HIGHER-DIMENSIONAL CAYLEY–DICKSON ALGEBRA

  • 期刊论文

  • 发表日期：

    2025年8月27日

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  • Doan Cong Dinh

摘要

Hypercomplex analysis is the extension of complex analysis to higher dimensions. In its development, besides Clifford analysis, the theory of functions taking values in non-associative Cayley–Dickson algebras has also been considered, especially octonion analysis. In this paper, we construct the Cauchy–Riemann operators in higher-dimensional Cayley–Dickson algebras. We prove the Cauchy integral formula and the Taylor series expansion for solutions of the Cauchy–Riemann operators.