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<p>The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of monogenic functions over real alternative <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-algebras has been introduced to unify several classical monogenic functions theories. In this paper, we initiate the study of monogenic functions of several hypercomplex variables over real alternative <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-algebras, which naturally extends the theory of several complex variables to a very general setting. In this new setting, we develop some fundamental properties, such as Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.</p>

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Monogenic Functions Over Real Alternative \(*\)-algebras: the Several Hypercomplex Variables Case

  • 期刊论文

  • 发表日期：

    2026年3月31日

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  • Zhenghua Xu,
  • Chao Ding,
  • Haiyan Wang

摘要

The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of monogenic functions over real alternative \(*\) ∗ -algebras has been introduced to unify several classical monogenic functions theories. In this paper, we initiate the study of monogenic functions of several hypercomplex variables over real alternative \(*\) ∗ -algebras, which naturally extends the theory of several complex variables to a very general setting. In this new setting, we develop some fundamental properties, such as Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.