Sufficient Conditions for Functions to Form Riesz Bases in L_2 and Applications to Nonlinear Boundary-Value Problems

Abstract

We find sufficient conditions for systems of functions to be Riesz bases in L2(0, 1). Then we improve a theorem presented in [13] by showing that a ``standard'' system of solutions of a nonlinear boundary-value problem, normalized to 1, is a Riesz basis in L2(0, 1). The proofs in this article use Bari's theorem.