循环矩阵集合中的函数类及其刻画
经典分析与常微分方程
2025-08-14 v3 交换代数
复变函数
摘要
本文引入新的函数类,推广了已知的复变函数类,如整函数、亚纯函数、有理函数与多项式函数,并使其取值于具有复数元素的循环矩阵集合。针对这些新函数类,我们将近期在 [Li, B. Q. Two elementary properties of entire functions and their applications. Amer. Math. Monthly 122(2) (2015), 169--172] 与 [Li, B. Q. A characterization of rational functions. Amer. Math. Monthly. 132(3) (2025), 269--271] 中得到的刻画定理推广到包含多个复变量的循环矩阵代数结构中。我们的刻画定理进一步推广了近期在 [Abramov, V. M. Extension of the fundamental theorem of algebra for polynomial matrix equation with circulant matrices. Amer. Math. Monthly. DOI: 10.1080/00029890.2024.2440298] 中所建立的代数基本定理的变体。
引用
@article{arxiv.2503.19049,
title = {Classes of functions in the set of circulant matrices and their characterization},
author = {Vyacheslav M. Abramov},
journal= {arXiv preprint arXiv:2503.19049},
year = {2025}
}
备注
11 pages, this version of the paper is final. It is accepted for publication in Ukrainian Mathematical Journal