Subadjoint equations of index-1 linear singular difference equations
The article deals with linear singular difference equations of the form \[ A_kx_{k+1} = B_kx_k, \quad k = 0,1,2,\ldots,N - 1,\tag{1} \] \(A_k, B_k \in {\mathbb R}^{m \times m}\), \(A_k\) are singular. Moreover, it is assumed that this equation is of index \(1\). Under these conditions it is proved that the subadjoint equation \[ A_{k-1}^Tu_k = B_k^Tu_{k+1}, \quad k = 0,1,2,\ldots,N - 1,\tag{2} \] is also of index \(1\). Also, the Lagrange identity discrete analogue and some relationships between equations (1) and (2) are obtained.
scientific article; zbMATH DE number 6168550