算子方程$ AX = C $和$ XB = D $的实正解

IF 1.2 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Networks and Heterogeneous Media Pub Date : 2023-01-01 DOI:10.3934/math.2023777

Haiyan Zhang, Yanni Dou, Weiyan Yu

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引用次数: 1

摘要

本文主要考虑Hilbert空间框架下的算子方程$ AX = C $和$ XB = D $。用收敛算子序列给出了AX = C $的简化解的一种新表示。研究了两个算子方程组$ AX = C $和$ XB = D $的公共解和公共实正解。给出了这些解的详细表示，用简短的证明扩展了经典的闭范围情形。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Real positive solutions of operator equations $ AX = C $ and $ XB = D $

In this paper, we mainly consider operator equations $ AX = C $ and $ XB = D $ in the framework of Hilbert space. A new representation of the reduced solution of $ AX = C $ is given by a convergent operator sequence. The common solutions and common real positive solutions of the system of two operator equations $ AX = C $ and $ XB = D $ are studied. The detailed representations of these solutions are provided which extend the classical closed range case with a short proof.

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来源期刊

Networks and Heterogeneous Media 数学-数学跨学科应用

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： NHM offers a strong combination of three features: Interdisciplinary character, specific focus, and deep mathematical content. Also, the journal aims to create a link between the discrete and the continuous communities, which distinguishes it from other journals with strong PDE orientation. NHM publishes original contributions of high quality in networks, heterogeneous media and related fields. NHM is thus devoted to research work on complex media arising in mathematical, physical, engineering, socio-economical and bio-medical problems.