Properties of solutions of an infinite system of ordinary linear differential equations of the first order with auxiliary boundary conditions

Abstract

where y(x) (yi(x)) is a vector in Hilbert space, i.e., E= converges and A (x) (A jj(x)) is a matrix each of whose elements is a Lebesgue summable function on X:O < x <1. Furthermore, the matrix A (x) is limited, in the sense defined by Hilbert, by a Lebesgue summable function 4(x) on X. In ?2 preliminary definitions are given and the system of notation used throughout the paper is explained. In ?3 the properties of matrices of functions which satisfy system (1) and the corresponding adjoint system are considered. The adjoint system is given by dzi 0 (2) dx= Aai(X)Za (i = 1,2, ... dx a=1