On classification of singular matrix difference equations of mixed order

Autor:	Zhu, Li, Sun, Huaqing, Xie, Bing
Rok vydání:	2022
Předmět:	Mathematics - Spectral Theory Mathematics - Classical Analysis and ODEs 34B20 39A27
Zdroj:	Proceedings of the Royal Society of Edinburgh: Section A Mathematics 154 (2024) 1235-1258
Druh dokumentu:	Working Paper
DOI:	10.1017/prm.2023.56
Popis:	This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness of initial value problems for these equations are derived, and then the classification of them is obtained with a similar classical Weyl's method by selecting a suitable quasi-difference. An equivalent characterization of this classification is given in terms of the number of linearly independent square summable solutions of the equation. The influence of off-diagonal coefficients on the classification is illustrated by two examples. In particular, two limit point criteria are established in terms of coefficients of the equation. Comment: 27 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.12708 Zobrazit plný text záznamu View this record from Arxiv