一般情况下的Vandermonde矩阵

IF 0.6 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2025-10-17 DOI:10.1134/S1064562424601914

A. I. Perov, I. D. Kostrub

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引用次数: 0

摘要

研究了任意复Banach代数中的Vandermonde矩阵。伴随的Frobenius矩阵用于建立代数方程的系数与由其根构造的Vandermonde矩阵之间的关系。在可逆Vandermonde矩阵的基础上定义了任意阶的可分差分。给出了一个类似于赫米特公式的可分差分的积分表示。给出了分差谱的一个包含和谱映射的邓福德定理的一个类比。

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Vandermonde Matrix in the General Case

The Vandermonde matrix is considered in an arbitrary complex Banach algebra. The accompanying Frobenius matrix is used to establish the relationship between the coefficients of an algebraic equation and the Vandermonde matrix constructed from its roots. The divided difference of arbitrary order is defined based on an invertible Vandermonde matrix. An analogue of the Hermite formula for an integral representation of the divided difference is given. An inclusion for the spectrum of the divided difference and an analogue of Dunford’s theorem on the mapping of spectra are given.

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来源期刊

Doklady Mathematics 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3-6 weeks

期刊介绍： Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.