Riesz bases in subspaces of L2(R+)

Abstract

In a recent investigation [8] concerning the asymptotic behavior of Gram-Schmidt orthonormalization procedure applied to the nonnegative integer shifts of a given function, the problem of determining whether or not such functions form a Riesz system in L2(R+) arose. In this paper, we provide a sufficient condition to determine whether the nonnegative translates form a Riesz system on L2(R+). This result is applied to identify a large class of functions for which very general translates enjoy the Riesz basis property in L2(R+).