On the basis property of root elements of ordinary differential operators in the space L 2,n (a, b)

Abstract

We study a spectral problem for a system of linear ordinary differential operators in the vector function space L 2,n (a, b) with parameter-dependent boundary conditions. We prove a theorem stating that the system of root functions of the problem is a basis with parentheses in L 2,n (a, b). Corollaries of the theorem are considered.