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<p>We introduce new classes of functions generalizing the well-known classes of functions of complex variable, such as the entire functions, meromorphic functions, rational functions, and polynomial functions, which take values in the set of circulant matrices with complex entries. For these new classes of functions, we extend some recently obtained characterization theorems presented in [B. Q. Li, <i>Amer. Math. Monthly</i>, <b>122</b>, No. 2, 169 – 172 (2015)] and [B. Q. Li, <i>Amer. Math. Monthly</i>, <b>132</b>, No. 3, 269 – 271 (2025)] to an algebraic structure of circulant matrices that includes several complex variables. Our characterization theorems generalize a recently established version of the fundamental theorem of algebra presented in [V. M. Abramov, <i>Amer. Math. Monthly</i>, <b>132</b>, No. 4, 356 – 360 (2025)].</p>

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Classes of Functions in the Set of Circulant Matrices and Their Characterization

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Vyacheslav M. Abramov

摘要

We introduce new classes of functions generalizing the well-known classes of functions of complex variable, such as the entire functions, meromorphic functions, rational functions, and polynomial functions, which take values in the set of circulant matrices with complex entries. For these new classes of functions, we extend some recently obtained characterization theorems presented in [B. Q. Li, Amer. Math. Monthly, 122, No. 2, 169 – 172 (2015)] and [B. Q. Li, Amer. Math. Monthly, 132, No. 3, 269 – 271 (2025)] to an algebraic structure of circulant matrices that includes several complex variables. Our characterization theorems generalize a recently established version of the fundamental theorem of algebra presented in [V. M. Abramov, Amer. Math. Monthly, 132, No. 4, 356 – 360 (2025)].