标题： 离散辛系统关于谱参数的一般线性依赖的本征函数展开 显示英文标题

标题： Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter

摘要： 离散辛系统在有限离散区间上的本征函数展开在关于谱参数的一般线性依赖情况下被建立，这是对Bohner、Došlý和Kratz在[Trans. Amer. Math. Soc. 361 (2009), 3109--3123]中给出的展开定理的重要推广。随后，通过使用合适的谱函数，显式地推导了Weyl--Titchmarsh$M({\lambda})$-函数的积分表示，并讨论了可能扩展到半直线情况的情形。主要结果通过几个例子进行了说明。 显示英文摘要

摘要： Eigenfunctions expansion for discrete symplectic systems on a finite discrete interval is established in the case of a general linear dependence on the spectral parameter as a significant generalization of the Expansion theorem given by Bohner, Do\v{s}l\'{y} and Kratz in [Trans. Amer. Math. Soc. 361 (2009), 3109--3123]. Subsequently, an integral representation of the Weyl--Titchmarsh $M({\lambda})$-function is derived explicitly by using a suitable spectral function and a possible extension to the half-line case is discussed. The main results are illustrated by several examples.