On the construction of linearly independent vectors with variable components

Abstract

We use the same notations as in a previous paper [1]. Let / be a closed interval \j, δl={t\γύtύδ, ίeR}. Let C(/, C) denote the totality of complexvalued functions defined and of class C μ on / (μ=0, 1, •••, oo). Hereafter we fix some μ.For the sake of brevity, we denote O(/, C) by K(J), and K(J) n by M(J):Let X{t) be an nXh matrix whose components all belong to K(J):

A remark on homogeneous linear equations with variable coefficients

“…1. We use the same notations as in previous papers [1], [2]. Let / be a closed interval [«, β] = {t I a^t^β, t(=R}.…”