Fredholm properties of a class of coupled operator matrices and their applications

IF 1.2 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2024-01-18 DOI:10.1007/s43034-024-00318-z

Jing Xu, Junjie Huang, Alatancang Chen

引用次数: 0

Abstract

This paper deals with Fredholm properties of the one-sided coupled operator matrix \({\mathcal {M}}=\left( \begin{array}{cc} A &{} B \\ 0 &{} D \end{array} \right) \left( \begin{array}{cc} I &{} 0 \\ L &{} I \end{array} \right)\) by means of generalized Schur factorization and the associated space decompositions. For \(\lambda \in {\mathbb {C}},\) some sufficient conditions are given for \(\lambda -{\mathcal {M}}\) to be Fredholm (resp. left or right Fredholm), and these conclusions are further used to determine the essential spectra of a delay equation and a wave equation with acoustic boundary conditions.

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一类耦合算子矩阵的弗雷德霍尔姆特性及其应用

Abstract This paper deals with Fredholm properties of the one-sided coupled operator matrix \({\mathcal {M}}=\left(\begin{array}{cc} A &{} B\\0 &；{D （end{array} \right） \left( （\begin{array}{cc} I &{} 0 （\L &{} I （end{array} \right））通过广义舒尔因式分解和相关的空间分解。对于 \(\lambda \in {\mathbb {C}}, \)，给出了 \(\lambda -{\mathcal {M}}\) 是弗雷德霍尔姆（左或右弗雷德霍尔姆）的一些充分条件，并进一步利用这些结论确定了延迟方程和带声学边界条件的波方程的本质谱。

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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来源期刊

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.